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REESE  LIBRARY 

OF  THE 


UNIVERSITY  OF  CALIFORNIA. 


Class 


'  Professional  Htfcrarg 

EDITED  BY  NICHOLAS   MURRAY  BUTLER 


THE   TEACHING   OF   PHYSICS 


THE  MACMILLAN  COMPANY 

NEW  YORK  •    BOSTON   •    CHICAGO 
DALLAS   •    SAN    FRANCISCO 

MACMILLAN  &  CO.,  LIMITED 

LONDON  •    BOMBAY  •    CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  LTD. 

TORONTO 


THE  TEACHING  OF  PHYSICS 


FOR 


PURPOSES  OF  GENERAL  EDUCATION 


BY 
C.    RIBORG    MANN 

ASSOCIATE  PROFESSOR  OF  PHYSICS 
THE  UNIVERSITY  OF   CHICAGO 


Itfefcr  gorfc 
THE    MACMILLAN   COMPANY 

1912 

All  rights  reserved 


COPYRIGHT,  1912, 
Bv  THE  MACMILLAN  COMPANY. 


Set  up  and  electrotyped.     Published  March,  1912. 


J.  8.  Cushing  Co.  —  Berwick  &  Smith  Go. 
Norwood,  Mass.,  U.S.A. 


TO   MY 

FATHER   AND   MOTHER 

WHOSE  WISE  AND   PRACTICAL  INTERPRETATION 

OF   LIFE 
MADE  THIS  BOOK  POSSIBLE 


236317 


AUTHOR'S    PREFACE 

ONE  of  the  liveliest  themes  of  present  educational 
discussion  is  that  of  the  distinction  between  vocational 
and  cultural  work.  According  to  the  old  ideas,  certain 
subjects  are  preeminently  cultural,  while  others  are 
distinctly  vocational ;  and  in  any  scheme  of  general 
education,  the  cultural  studies  must  predominate.  The 
present  insistent  demand  for  industrial  training  has 
brought  these  ideas  into  the  limelight  of  investigation, 
and  has  divided  the  forces  of  education  into  two  parties, 
which  may  be  called  the  culturalists  and  the  vocation- 
alists. 

This  distinction  between  cultural  and  vocational  seems 
to  be  wholly  beside  the  mark  in  any  true  system  of 
general  education.  It  owes  its  origin  to  the  mistaken 
ideas  of  the  doctrine  of  formal  discipline.  This  book  is ' 
an  effort  to  show  how,  in  the  case  of  physics,  the  two 
points  of  view  may  be  amalgamated  into  one.  The 
fundamental  thesis  of  this  union  has  been  stated  by 
President  G.  Stanley  Hall,  in  his  Educational  Problems, 
in  the  following  words  (Vol.  I,  p.  614) :  "  In  point  of 
fact,  we  psychologists  must  make  the  mortifying  con- 

vii 


Vlii  AUTHOR'S  PREFACE 

fession  that  we  know  almost  nothing  of  pure  culture 
values,  either  what  they  are  or  how  to  acquire  them. 
But  we  do  know  that  to  succeed  an  individual  must 
put  his  whole  soul  into  his  work,  and  that  the  study  of 
even  Greek,  Latin,  and  logic  in  a  half-hearted  way  is 
demoralizing  and  soporific.  We  know,  too,  that  if  most 
men  do  not  find  culture  value  in  their  own  vocation  they 
will  never  find  it.  Anything  is  cultural  that  arouses 
the  ambition  of  young  people  to  do  their  best;  hence 
whether  a  topic  is  cultural  or  practical  depends  wholly 
upon  the  point  of  view  and  the  spirit." 

The  book  is  divided  into  three  parts.  The  first  of 
these  traces  the  development  of  the  present  situation. 
The  second  traces  the  origin  of  physics,  and  seeks  to 
establish  its  leading  characteristics  and  to  define  its 
possibilities  as  a  means  of  general  education.  In  the 
third  part  the  purpose  of  physics  teaching  is  stated,  and 
hints  are  given  as  to  how  this  purpose  may  be  attained. 

The  physics  teacher  will  doubtless  find  this  third 
part  unsatisfactory  in  that  it  gives  few  specific  directions 
as  to  how  to  proceed.  The  reason  for  this  is  obvious. 
Physics  teaching  has  suffered  in  the  past  from  over- 
specification.  While  it  is  true  that  young  teachers 
want  to  be  told  in  detail  just  what  to  do,  it  is  equally 
true  that  such  detailed  instructions  are  a  very  serious 
obstacle  to  effective  work.  Every  successful  teacher 


AUTHOR'S  PREFACE  ix 

must  think  for  himself  and  adapt  his  work  to  his  special 
environment.  A  detailed  specification  of  just  what  to 
do  is  incompatible  with  the  educational  ideas  expressed 
in  this  book. 

In  addition  to  the  references  given  as  footnotes  to  the 
text,  the  chapters  in  Parts  II  and  III  are  supplied  with 
lists  of  "collateral  reading."  In  order  to  make  these 
lists  brief,  they  include  in  general  only  references  to 
works  published  within  the  past  ten  or  twelve  years. 
Older  works  are  included  when  they  contain  material 
that  has  not  been  dealt  with  more  briefly  in  recent 
writings. 

The  author  wishes  here  to  express  his  sense  of  deep 
obligation  to  the  many  hundred  physics  teachers  who, 
by  correspondence  and  discussion,  have  contributed 
ideas  to  the  New  Movement  among  Physics  Teachers, 
of  which  this  book  is  the  outcome.  He  also  wishes 
especially  to  record  his  obligation  to  the  editor  of  this 
series,  President  Nicholas  Murray  Butler,  of  Columbia 
University,  and  to  Professor  J.  F.  Woodhull,  of  Teachers 
College,  New  York,  Professor  O.  W.  Caldwell  of  the 
University  of  Chicago,  and  Professor  G.  R.  Twiss,  of 
Ohio  State  University,  for  their  many  valuable  criticisms 
and  suggestions  made  while  the  book  was  in  manuscript 

and  in  press. 

C.  R.  MANN. 
THE  UNIVERSITY  or  CHICAGO, 
January,  1912. 


TABLE   OF   CONTENTS 

FAGBS 

AUTHOR'S  PREFACE       .        .        .        .  .        .        .  vii-ix 

EDITOR'S  INTRODUCTION xv-xviii 

INTRODUCTION xix-xxv 

PART    I 

THE  DEVELOPMENT  OF  THE  PRESENT  SITUATION 

CHAPTER   I 

THE  BACKGROUND 1-24 

The  Purpose  of  the  Public  High  School  —  Expansion 
of  the  High  School  —  The  Committee  of  Ten  —  The  Com- 
mittee on  College  Entrance  Requirements  —  Predomi- 
nance of  Small  High  Schools  —  Elimination  from  High 
Schools  —  Recent  Tendencies. 

CHAPTER  II 

NATURAL  PHILOSOPHY 25-40 

University  Physics  —  Natural  Philosophy  —  Old  Texts 
of  Natural  Philosophy  —  Modern  High  School  Physics. 

CHAPTER  III 

PRESCRIBED  PHYSICS 41-?2 

Early  High  School  Physics  —  The  Nature  of  the  Course 
in  1884  — Opinions  on  the  Method  of  Teaching  Physics 
in  1884— The  First  Syllabus  — The  Harvard  Descriptive 
List  — The  Committee  of  Ten  — The  National  Physics 
Course  — The  New  York  State  Syllabus  —  The  North 
Central  Syllabus  —  Uses  and  Abuses  of  Syllabi. 


xii  TABLE  OF  CONTENTS 

CHAPTER   IV 

PAGES 

TEXTBOOKS,  OLD  AND  NEW 73~95 

The  Problem  not  yet  Solved  — The  Method  of  the 
Texts,  Definitions  —  General  Statements  —  Experiments 
Precede  —  Generalized  Bodies  —  General  Theories  Pre- 
cede —  Laboratory  Manuals  —  Conclusions. 

PART   II 

PHYSICS  AND  DEMOCRATIC  EDUCATION 
CHAPTER   V 

THE  PEDIGREE  OF  PHYSICS 96-124 

Plato  —  Aristotle  —  Art  precedes  Science  —  Develop- 
ment of  Industry  —  Method  of  Industry  —  Germanic  In- 
dustry—  The  Parents  of  Physics  —  The  Renaissance  — 
Archimedes  —  Galileo  and  Guttenberg  —  Scientific  In- 
dustry—The Methods  of  Science. 

CHAPTER  VI 

THE  METHOD  OF  PHYSICS 125-148 

Method  is  Characteristic  —  Scientific  Training  not 
Transferable  —  Definitions  of  the  Method  of  Science  — 
The  Real  Method  —  Logic  follows  Intuition  —  The  Con- 
crete and  the  Abstract  —  Wide  Association  Necessary  — 
The  Place  of  Applications  — The  Method  of  Physics  — 
The  Truth  of  Physical  Laws. 

CHAPTER  VII 

THE  BIOGRAPHY  OF  PHYSICS        .        .        .        .  149-169 

What  are  the  Characteristics  of  Physics  ?  —  Galileo's 
Work  —  The  Causal  Principle  —  Perpetual  Motion  — 
Newton's  Work  —  Newton's  Successors  —  The  Introduc- 
tion to  Mechanics  —  The  Advent  of  the  Steam  Engine 
—  The  Conservation  of  Energy  —  Energy  in  Physics  and 
in  Industry  —  Work  precedes  Logic. 


TABLE   OF   CONTENTS  xiij 

CHAPTER  VIII 

PACKS 

THE  DISCIPLINE  OF  PHYSICS 170-197 

The  Doctrine  of  Formal  Discipline  —  The  Work  in 
Modern  Languages  —  Formal  Discipline  in  Science  — 
Peculiarities  of  the  Doctrine — Formal  Discipline  in  Physics 

—  Psychology  to  the  Rescue  —  The  Problem  of  Transfer 
of  Training  —  Training  is  Specific  —  Specific  Discipline 
sometimes  Transferable  —  Identical   Elements  —  Subject 
Matter  —  Method  —  Ideals  of  Method  —  The  Emotional 
Element  — The  Intellectual  Feeling  of  Wonder  — True 
Discipline  requires  Motivation. 

PART   III 

HINTS  AT  PRACTICAL  APPLICATIONS 

CHAPTER   IX 

THE  CONCRETE  PROBLEM 198-217 

Importance  of  Daily  Experiences  —  Industrial  Study  of 
Science  — The  Administrative  System  —  The  Needs  of 
the  Masses  —  Syllabi  do  not  solve  the  Problem  —  Experi- 
mentation Needed  —  Problems  needing  Experimental  So- 
lutions —  Summary  of  Conclusions  —  Bringing  Physics 
close  to  the  Daily  Life  —  The  Purpose  of  Physics  Teach- 
ing—  The  Prejudices  of  Education. 

CHAPTER  X 

THE  ORGANIZATION  OF  THE  COURSE    ....     218-245 

Simplicity  and  Unity  —  Mechanism  —  The  Fundamental 
Principles  —  Objectivity  Necessary  —  Definitions  —  How 
define  Work  —  Problems  that  require  Measurement  — 
Efficiency  —  Summary  :  The  Work  Principle  —  Problems 
in  Heat  —  Definition  of  Energy  —  The  Energy  Principle 

—  Some  Objections  —  Optics  —  Theories  Unnecessary  — 
Light  and  Electricity  —  Remember  the  Aim,  Unity. 


TABLE  OF  CONTENTS 
CHAPTER  XI 

PAGES 

THE  LABORATORY  WORK 246-269 

Current  Ideas  of  Laboratory  Work  —  Current  Ideas  are 
Inadequate  —  The  Result  should  be  Significant  —  The 
Real  Purpose  —  Conditions  for  Vital  Work  —  Suitable 
Problems  —  Engineering  or  Physics  —  Go  from  Concrete 
to  Abstract  — The  Psychological  and  the  Logical. 

CHAPTER  XII 

TESTING  RESULTS 270-289 

Current  Forms  of  Test  —  Questions  not  Significant  — 
Vital  Problems  Needed  —  Ordinary  Examinations  Ineffi- 
cient —  More  Definite  Tests  —  Tests  help  the  Teacher  — 
Summary  —  More  Efficient  Teaching  demands  Educational 
Experiments. 

BIBLIOGRAPHY 291-299 

INDEX 301-304 


EDITOR'S    INTRODUCTION 

THERE  is  a  good  deal  to  be  said  on  the  subject  of 
teaching  physics  in  secondary  schools  and  to  students 
of  the  elements  of  physical  science  in  colleges,  that  can 
properly  be  said  by  one  who,  though  not  a  physicist,  is 
an  observer  and  student  of  contemporary  educational 
conditions  and  problems.  Certain  fundamental  princi- 
ples ought  to  be  assumed. 

1.  The  topics  chosen  and  the  method  pursued  should 
be  determined  by  the  intellectual  needs  and  interests  of 
pupils  of  secondary  school  age,  and  not  by  some  pre- 
conceived notion  as  to  what  those  needs  and  interests 
ought  to  be.     College  admission  tests  in  physics  should 
be  made  to  depend  upon  the  secondary  school  teaching 
of  that  subject,  when  properly  organized  and  conducted, 
and  not  vice  versa. 

2.  The  teacher  should  put  out  of  his  mind  the  thought 
that  each  pupil  before  him  is  aiming  to  become  a  special- 
ist in  physical  science,  or  that  the  study  of  physics  is 
his  main  interest  in  life. 

3.  Physical  science  should  not  be  presented  as  some- 
thing fixed  and  definite,  whose  conclusions  are  final,  but 


xvi  EDITOR'S  INTRODUCTION 

rather  as  a  division  of  organized  knowledge  which  is 
constantly  expanding  and  developing  and  which  has 
frequently,  within  historic  times,  corrected  its  conclu- 
sions in  the  light  of  later  discoveries.  To  this  end  some 
outline  of  the  history  of  physical  science  and  of  the  time 
and  order  in  which  its  fundamental  laws  were  discovered 
and  developed  should  be  given  to  the  student.  Wher- 
ever it  is  possible  to  relate  the  discovery  or  new  appli- 
cation of  a  physical  principle  to  man's  other  activities, 
this  should  be  done  in  order  that  the  student  may  be 
made  to  feel  from  the  beginning  the  intimate  relation 
between  the  laws  and  phenomena  with  which  physics 
deals,  and  other  human  interests.  In  other  words,  the 
teaching  of  physics  should  be  humanized. 

4.  As  a  farther  step  in  the  humanizing  of  physics 
teaching,  the  pupil  should  be  brought  to  know  some- 
thing of  the  men  whose  names  are  epoch-marking  in  the 
history  of  physical  science.     Such  names  as  those  of 
Archimedes,  Galileo,   Newton,   Kepler,  Gauss,  Young, 
Gay-Lussac,  Davy,  Faraday,  Helmholtz,  Kelvin,  Torri- 
celli,  Ampere,  Joule,   Mayer,   Fresnel,   Galvani,  Volta, 
should  be  familiar  to  the  student,  and  he  should  be  able 
to  tell  something  of  who  these  men  were,  when  they 
lived,  and  what  they  did  which  causes  them  to  be  re- 
membered in  the  history  of  science. 

5.  By  material  drawn  from  the  third  book  of  John 
Stuart  Mill's  "  Logic,"  or  from  Professor  Jevons's  "  Prin- 


EDITOR'S  INTRODUCTION  xvii 

ciples  of  Science,"  the  skillful  teacher  may  so  interest 
the  student  in  his  laboratory  problems  that  the  student 
will  come  to  understand  clearly  the  significance  of  the 
inductive  method,  of  the  verification  of  hypotheses,  and 
of  the  formulation  of  so-called  laws  of  nature. 

6.  The  ordinary  standards  for  measuring  time,  space, 
weight,  and  other  characteristics,  should  not  be  taken 
for  granted,  but  their  origin  and  history  should  be  made 
plain  and  their  fundamental  principles  discussed.     Un- 
der this  head  I  would  include  also  the  thermometer, 
the  barometer,  the  microscope,  the  telescope,  and  the 
spectroscope. 

7.  It  is  difficult  for  one  not  himself  a  physicist  to 
make  any  profitable  suggestions  as  to  the  subjects  to  be 
selected  for  presentation  to  students  of  physics  in  sec- 
ondary schools.     In  general,  however,  it  may  safely  be 
held  that  these  subjects  should  be  those  general  ones 
which  relate  in   an   elemental  or  fundamental  way  to 
transformations  of  energy.     The  tendency  observable 
in  many  school  textbooks  to  pursue  these  subjects  into 
very  refined  and  subtle  inferences,  is  to  be  deprecated. 
Taught  in  this  way  the  beginner  loses  his  sense  of  per- 
spective and  physics  repels  rather  than  attracts  him. 

8.  Far  too  much  has  been  made  in  recent  years  of 
accuracy  of  measurement  in  the  teaching  of  elementary 
physics.     It  is  much  more  important  to  throw  emphasis 
upon  the  descriptive  aspects  of  the  science  and  to  feed 


xviii  EDITOR'S  INTRODUCTION 

the  growing  mind  with  food  that  really  interests  it  and 
helps  it  to  grow,  than  to  pursue  the  will-o'-the-wisp  of 
training  some  imaginary  power  of  habitual  accuracy. 
Accurate  measurements  have  their  place  in  the  teach- 
ing of  elementary  physics,  but  that  place  is  a  subordi- 
nate one.  The  main  task  is  to  teach  the  constitution 
and  behavior  of  matter,  as  it  presents  itself  to  the 
human  power  of  perception,  and  the  laws  of  motion  as 
these  have  been  observed  and  deduced,  together  with 
the  relation  of  these  to  man  and  his  activities. 

NICHOLAS  MURRAY  BUTLER. 

COLUMBIA  UNIVERSITY, 
February  I,  1912. 


INTRODUCTION 

IN  one  of  the  large  high  schools  of  this  country,  two 
girls,  members  of  the  physics  class,  were  counting  the 
swings  of  a  large  pendulum  that  was  suspended  in  a 
doorway.  On  being  asked  by  a  visitor  what  they  were 
doing,  they  replied,  "  Measuring  the  specific  gravity  of 
the  city."  When  they  were  questioned  as  to  whether 
the  result  would  be  expressed  in  pounds,  in  cubic  yards, 
in  seconds,  or  in  inches,  they  answered  that  they  did  not 
know. 

A  student  in  a  college  class  of  physics,  having  made 
an  experiment  intended  to  measure  the  acceleration  of 
gravity,  brought  in  the  result  967.  When  asked 
"967  what  ?  "  he  promptly  replied,  "  Dynes  per  centi- 
meter per  centimeter." 

When  we  consider  the  importance  that  is  usually 
attached  to  the  subject  of  accelerated  motion  and  the 
amount  of  time  that  is  generally  devoted  to  it  in  physics 
classes,  the  following  experience  may  prove  instructive. 
At  one  of  the  large  universities  a  scholarship  examina- 
tion in  physics  was  given.  Twenty-five  candidates 
from  fourteen  excellent  schools  presented  themselves  to 


XX  INTRODUCTION 

take  the  test.  Since  the  winning  of  the  scholarship  was 
an  honor  to  the  school,  as  well  as  a  financial  reward  to 
the  winner,  only  those  pupils  whose  work  in  physics 
in  the  schools  had  been  most  satisfactory  entered  the 
competition.  One  of  the  questions  on  the  examination 
paper  was  this:  A  block  slides  without  friction  down 
an  inclined  plane  of  height  50  cm.  and  of  length,  measured 
along  the  incline,  of  100  cm.  What  velocity  will  it  have 
when  it  reaches  the  bottom? 

Only  two  of  the  twenty-five  competitors  gave  the 
correct  solution.  One  of  the  pupils  answered:  — 

Velocity  =152,  or  2  cm.  per  second. 
5°   . 

Another  solved  it  in  this  way :  — 
W:P::L:H 
i  :P  ::  ioo : 5 
^  =  •5 

.5  X  ioo  =  50  =  change  in  velocity.  50  =  velocity 
at  the  bottom,  since  a  force  of  .5  will  be  acting  on  it 
through  ioo  cm. 

While  the  foregoing  are,  perhaps,  extreme  cases,  every 
physics  teacher  knows  that  answers  of  this  sort  are  very 
common  —  too  common  to  be  ignored.  Some  teachers, 
to  bevsure,  still  comfort  themselves  with  the  belief  that 
the  same  failure  to  gain  clear  ideas  is  equally  prevalent 


INTRODUCTION  xxi 

in  other  studies;  and  that  it  is,  therefore,  a  necessary 
characteristic  of  a  large  group  of  students.  But  the 
majority  of  teachers  have  now  waked  up  to  the  fact  that 
such  answers  are  indicative  of  a  condition  that  needs 
study  and,  if  possible,  correction.  The  way  in  which 
the  bibliography  of  physics  teaching  has  increased  during 
the  last  decade  is  ample  proof  of  the  fact  that  a  large 
and  continually  increasing  number  of  physics  teachers 
are  now  seriously  studying  this  subject  in  an  effort  to 
find  out  what  is  the  matter  and  how  better  results  may 
be  secured. 

As  is  unavoidable  at  the  beginning  of  the  scientific 
study  of  any  relatively  new  and  very  complex  situation, 
many  radically  different  hypotheses  have  been  advanced 
to  explain  the  phenomenon  and  aid  in  obtaining  a 
solution  of  the  problem.1  Not  only  are  these  hypotheses 
numerous,  but  the  terms  in  which  they  are  stated  are 
usually  not  defined  with  any  definiteness.  For  example, 
most  teachers  agree  that  "  physics  should  be  brought 
close  to  the  daily  life  of  the  pupils  " ;  but  there  are  as 
many  different  interpretations  of  this  phrase  as  there 
are  teachers.  Each,  then,  takes  his  own  interpretation 

1  For  a  summary  of  some  of  these  suggestions,  see  Circular  II  of  the 
New  Movement  among  Physics  Teachers,  School  Review,  XIV,  p.  429 ; 
June,  1906;  also  Symposium  on  the  Purpose  of  Physics  Teaching,  School 
Science  and  Mathematics,  VIII,  p.  718 ;  IX,  pp.  1,162;  291,  Dec.,  1908; 
Jan.,  Feb.,  March,  1909. 


xxii  INTRODUCTION 

as  complete ;  and  so,  while  there  seems  to  be  agreement, 
there  is  no  real  or  helpful  solution  of  the  problem.  Just 
exactly  what  is  "  physics  "  ?  and  precisely  what  does 
"  bringing  it  close  to  the  lives  of  the  pupils  "  mean 
anyhow  ? 

A  moment's  thought  will  convince  any  one  that  the 
current  definitions  of  physics,  such  as  "  Physics  is  the 
science  of  matter  and  energy,"  or  "  Physics  is  the  science 
of  phenomena,"  do  not  assist  the  teacher  who  is  seriously 
seeking  to  find  out  specifically  just  what  he  is  trying 
to  bring  close  to  the  lives  of  his  pupils.  Such  definitions 
may  be  useful  in  distinguishing  physics  from  chemistry 
or  biology,  but  they  do  not  really  define  physics  until  the 
more  general  terms  science,  matter,  energy,  etc.,  have  been 
defined.  It  is  not,  for  example,  particularly  helpful  to 
any  one  to  introduce  the  subject,  as  one  recent  text 
does,  by  saying:  "  Physics  is  the  science  of  matter  and 
energy.  In  order  to  understand  this  definition,  we 
must  know  what  matter  is.  Nobody  knows  what  matter 


is." 


Spencer's  definition  of  science  as  "  classified  knowl- 
edge "  leads  nowhere;  not  only  because  it  implies  an 
understanding  of  what  knowledge  is,  but  also  because, 
as  Dewey  has  shown,1 "  it  is  wholly  ambiguous.  Does  it 

1  Dewey,  Science  as  Subject-Matter  and  as  Method,  Science,  Vol. 
XXXI,  p.  125,  Jan.  28,  1910. 


INTRODUCTION  Xxiii 

A-*" 
mean  the  body  of  facts,  the  subject  matter  ?     Or  does  it 

mean  the  processes  by  which  something  fit  to  be  called 
knowledge  is  brought  into  existence,  and  order  intro- 
duced into  the  flux  of  experience  ?  That  science  means 
both  of  these  things  will  doubtless  be  the  reply,  and 
rightly.  But  in  order  both  of  time  and  of  importance, 
science  as  method  precedes  science  as  subject  matter. 
Systematized  knowledge  is  science  only  because  of  the 
care  and  thoroughness  with  which  it  has  been  sought  for, 
selected,  and  arranged.  Only  by  pressing  the  courtesy 
of  language  beyond  what  is  decent,  can  we  term  such 
information  as  is  acquired  ready-made,  without  active 
experimenting  and  testing,  science." 

If  science  is  not  only  "  systematized  knowledge,"  but 
also  those  "  processes  by  which  something  fit  to  be 
called  knowledge  is  brought  into  existence,"  an  under- 
standing of  the  term  involves  an  understanding  of  those 
processes.  Hence  the  teacher  who  would  clearly  know 
what  he  is  trying  to  do  is  at  once  launched  upon  a 
sea  of  metaphysics  and  psychology.  He  finds  himself 
afloat  without  a  pilot  on  the  ocean  of  literature  that 
deals  with  this  subject  and  extends  from  Aristotle's 
Organon  to  Dewey's  How  We  Think,  —  an  ocean  whose 
shores  are  lined  with  shoals  of  "  muddy  speculation  " 
and  strewn  with  the  wreck  of  many  a  cherished  system. 

But  if  an  understanding  of  the  meaning  of  science  is 


xxiv  INTRODUCTION 

so  fraught  with  danger,  what  shall  we  say  of  the  terms 
matter  and  energy?  Are  there  any  buoys,  beacons,  or 
charts  that  can  help  to  steer  a  rational  course  here? 
And  how  shall  we  discover  a  useful  idea  of  what  is 
meant  by  the  "  life  of  the  pupils  "  to  which  "  physics  " 
must  be  "  brought  close  "  ?  Is  this  daily  life  the  daily 
routine  of  experiences  with  materials  ?  Or  is  it  the 
feelings  of  the  pupils,  or  their  intellectual  reaction  that 
is  meant  ?  Or  is  it  all  of  these  together  ?  Also,  what  is 
the  process  by  which  "  physics  "  and  "  daily  life  "  may 
be  brought  together  ? 

The  preceding  questions  have  been  raised,  not  for  the 
purpose  of  introducing  a  "  theoretical  "  discussion  of 
the  teacher's  problem,  nor  yet  with  any  idea  of  answer- 
ing them  in  the  following  chapters.  They  are  placed 
here  for  the  purpose  of  inducing  a  proper  state  of  humility 
and  open-mindedness  on  the  part  of  the  reader  for  what 
follows.  These  questions  have  not  yet  been  answered; 
possibly  they  never  will  be.  Yet  an  appreciation  of  the 
fact  that  they  are  ever  with  us  is  a  very  effective  preven- 
tive of  dogmatism,  and  the  scientific  study  of  them  is 
always  of  great  practical  use. 

It  is  the  purpose  of  this  book  to  demonstrate  the  fact 
that  the  study  of  these  insoluble  problems  of  life  is  of 
the  greatest  practical  use  to  the  teacher,  by  pointing  out 
a  few  of  the  many  cases  in  which  this  is  true.  For  this 


INTRODUCTION  XXV 

purpose  these  problems  will  be  discussed  only  so  far  as 
their  discussion  seems  likely  to  help  teachers  in  their 
ever-present,  everyday,  practical  problem  of  "  what 
shall  I  do,  and  how  shall  I  do  it  ?  " 


THE  TEACHING  OF  PHYSICS 

PART   I 

THE  DEVELOPMENT  OF   THE   PRESENT 
SITUATION 

CHAPTER  I 

THE  BACKGROUND 

i.  Ptfrpose  of  the  Public  High  School.  —  As  a  first 
step  in  the  discussion  of  the  problems  roughly  sketched 
in  the  introduction,  it  will  be  well  to  consider  the  general 
development  of  the  public  high  schools  in  the  United 
States.  Since  the  growth  of  physics,  like  that  of  every 
other  subject  in  the  high-school  course,  has  been  part  and 
parcel  of  this  general  development,  a  preliminary  glance 
at  the  large  outlines  of  the  whole  furnishes  a  background 
for  the  better  understanding  of  the  parts.  This  outline 
will  be  brief,  touching  only  the  high  points  in  the  story. 
Those  who  wish  a  more  detailed  history  of  the  movement 
for  public  high  schools  are  referred  to  the  excellent  work 
of  E.  E.  Brown  on  The  Making  of  Our  Middle  Schools 
(Longmans,  Green,  &  Co,,  1902). 


2  THE  TEACHING  OF  PHYSICS 

The  development  of  the  private  secondary  schools  and 
academies  will  not  here  be  considered.  The  point  of 
view  to  be  maintained  throughout  is  that  of  the  public 
high  school,  as  first  defined  by  Benjamin  Franklin  in  1743. 
In  his  Proposals  Relating  to  the  Education  of  the  Youth  of 
Pennsylvania,  he  says :  "  As  to  their  studies,  it  would  be 
well  if  they  could  be  taught  everything  that  is  useful,  and 
everything  that  is  ornamental.  But  art  is  long  and  their 
time  is  short.  It  is  therefore  proposed,  that  they  learn 
those  things  that  are  likely  to  be  most  useful  and  most 
ornamental ;  regard  being  had  to  the  several  professions 
for  which  they  are  intended."  1 

This  point  of  view  finds  more  general  definition  in  the 
words  of  Brown : 2  "  The  high  schools,  on  the  other  hand, 
appeal  less  to  imagination  and  sentiment  (than  do  the 
academies).  Their  promoters  did  not  set  about  doing 
good  to  the  people,  but  rather  undertook  to  work  with 
all  the  people  for  the  common  good.  Here,  too,  we  touch 
one  of  the  finest  things  in  all  the  world,  the  spirit  which 
draws  men  together  in  a  common  pursuit  of  the  public 
welfare." 

In  a  word,  the  high  school  was  founded  as  part  of  the 
new  democracy,  its  special  function  being  that  of  doing, 
in  the  field  of  education,  its  full  share  in  solving  the  hith- 
erto unsolved  problems  of  democracy. 

1  Brown,  Making  of  Our  Middle  Schools,  p.  180.        2  Ibid.,  p.  321. 


THE  BACKGROUND  3 

This  being  the  special  function  of  the  public  high  school, 
the  problem  of  the  physics  teacher  is  not  simply  that  of 
making  his  pupils  learn  that  body  of  organized  knowledge 
now  called  "physics."  It  is  rather  that  of  finding  out 
how  the  science  of  physics  may  be  made  to  contribute 
most  efficiently  to  the  development  of  democracy.  From 
this  point  of  view,  the  teacher  is  no  longer  a  mere  teacher 
of  physics  ;  he  is  rather  one  of  the  large  army  of  those  who 
are  laboring  for  the  attainment  of  the  highest  possible 
social  efficiency. 

2.  Early  High  Schools.  —  Although  the  need  for  this 
sort  of  public  high  school  was  set  forth  by  Benjamin 
Franklin  in  1743,  and  although  his  efforts  were  rewarded 
by  the  establishment  of  the  "  Public  Academy  in  the 
City  of  Philadelphia  "  in  1751,  the  real  movement  for 
public  high  schools  began  with  the  establishment  of  the 
English  Classical  School  in  Boston,  in  1821.  This  was 
followed  by  the  opening  of  the  High  School  for  Boys  in 
New  York  in  1825  ;  the  Central  High  School  in  Phila- 
delphia in  1838  ;  and  the  High  School  in  Baltimore  in 


These  early  high  schools  were  independent  schools, 
each  established  voluntarily  by  the  city  that  supported 
it.  In  the  West,  the  high  schools  grew  up  in  general 
under  state  systems  of  education,  in  which  the  state  re- 

1  Brown,  I.e.,  pp.  297  sq, 


4  THE  TEACHING  OF  PHYSICS 

quired  the  towns  to  establish  schools  in  conformity  with 
a  system  whose  ideal  was  "a  more  general  system  of 
education,  ascending  in  regular  gradation  from  township 
(district)  schools  to  a  state  university,  wherein  tuition 
shall  be  gratis  and  equally  open  to  all."  *  It  is  this 
sentiment  at  the  basis  of  American  educational  systems 
that  gave  in  later  times  such  importance  to  the  college 
entrance  requirements.  Since  the  university  was  re- 
garded as  the  infallible  head  of  the  system,  the  high 
schools  felt  themselves  compelled  to  meet  these  require- 
ments in  order  to  keep  the  path  open  for  all  from  the 
kindergarten  to  the  university. 

In  the  fifty  years,  from  1840  to  1890,  the  number  of 
public  high  schools  gradually  increased  to  2526,  with 
202,963  pupils.  This  was  for  them  a  period  of  struggle 
for  popular  recognition.  There  are  records  of  lawsuits, 
like  the  Kalamazoo  case  in  1872,  in  which  the  taxpayers 
questioned  the  right  of  school  authorities  "  to  levy  taxes 
upon  the  general  public  for  the  support  of  what  in  this 
state  (Michigan)  are  known  as  high  schools,  and  to  make 
free  by  such  taxation  the  instruction  of  children  in  other 
languages  than  the  English."  In  this  case,  it  was  argued 
that  "  the  general  understanding  of  the  people  has 
been  such  as  to  require  us  to  regard  the  instruction  in 
the  classics  and  in  the  living  modern  languages  in  these 

1  Brown,  l.c.,  p.  349. 


THE  BACKGROUND  5 

schools  as  in  the  nature  not  of  practical  and  therefore 
necessary  instruction  for  the  benefit  of  the  people  at 
large,  but  rather  as  accomplishments  for  the  few,  to  be 
sought  after  in  the  main  by  those  best  able  to  pay  for 
them,  and  to  be  paid  for  by  those  who  seek  them,  and 
not  by  general  tax."  1 

3.  Expansion  of  the  High  School.  —  Notwithstanding 
these  objections,  the  high  schools  gradually  developed 
in  popular  favor.  Since  1890,  the  increase  in  their 
number  has  been  phenomenal.  In  1900  there  were  more 
than  6000,  with  over  530,000  pupils;  and  in  1910  this 
number  had  been  increased  to  10,213  schools,  with 
915,061  pupils.  In  this  period  the  number  of  pupils 
increased  from  0.36  per  cent  to  1.03  per  cent  of  the 
total  population  of  the  country.  The  buildings,  grounds, 
and  equipment  used  by  these  schools  were  valued  in 
1910  at  more  than  $230,000,000;  something  like  $60,- 
000,000  was  spent  that  year  for  new  buildings  and 
improvements;  and  the  running  expenses,  while  they 
cannot  be  accurately  given,  were  certainly  not  less 
than  $40,000,000  for  the  year.2 

Although  the  United  States  Bureau  of  Education 
began  issuing  its  reports  in  1871,  the  public  high  schools 
appear  at  that  time  to  have  been  of  too  little  importance 

1  Brown,  I.e.,  p.  357. 

2  Report  of  the  United  States  Bureau  of  Education  for  1910,  II,  p.  1132. 


6  THE  TEACHING  OF  PHYSICS 

to  have  their  statistics  included  in  those  reports.  These 
statistics  first  appear  in  the  report  for  1876,  and  no  effort 
was  made  to  make  them  complete  until  1889.  The  year 
1876  may  then  be  taken  as  the  beginning  of  that  rapid 
development  that  has  just  been  noted.  Whatever  the 
schools  may  have  been  prior  to  1876,  they  seem  by  that 
time  to  have  fallen  completely  under  the  spell  of  the  idea 
that  the  course  of  study  that  led  to  college,  as  defined 
by  the  entrance  requirements  issued  by  the  colleges,  was 
the  highest  type  of  course  that  they  could  give.  As 
Brown  puts  it:  "  But  the  high  schools  gravitated  to- 
ward the  colleges  as  the  academies  had  done  before  them. 
None  of  the  many  protests  raised  against  this  movement 
could  check  it  for  any  length  of  time.  It  was,  in  fact,  a 
thoroughly  American  movement.  It  answered  to  that 
broad,  American  logic  which  maintained  that  since  any 
youth  might  rise  to  the  highest  offices,  every  youth 
should  have  the  opportunity  offered  to  him  of  rising  to 
the  highest  education."  1 

Notwithstanding  the  fact  that  the  high  schools  were 
founded  largely  for  the  purpose  of  training  those  who 
were  not  destined  for  college  to  greater  efficiency  in 
life,  there  is,  with  the  possible  exception  of  the  manual 
training  movement,  which  began  about  this  time  (1879), 
little  evidence  that  the  high  schools  made  any  serious 
1  Brown,  I.e.,  p.  373- 


THE  BACKGROUND  7 

efforts  to  study  their  magnificent  problem  of  demo- 
cratic education.  Their  energies  seem  to  have  been 
exhausted  in  the  process  of  mere  physical  growth,  and 
in  keeping  pace  with  the  expansion  of  the  institutions 
of  higher  learning  whose  feeders  they  were. 

This  was  a  period  of  great  educational  activity  and 
expansion  on  all  sides.  The  colleges,  under  the  pressure 
of  the  scientific  and  commercial  activities  about  them, 
were  adding  new  subjects  to  their  curricula  and  ex- 
panding their  science  courses  to  keep  up  with  the  general 
growth.  New  courses  were  introduced;  and  new  de- 
grees, Ph.B.,  LL.B.,  S.B.,  etc.,  were  invented  to  indi- 
cate that  these  new  courses,  while  meriting  recogni- 
tion, could  not  possibly  give  that  peculiar  "culture" 
and  that  formidable  "  mental  discipline "  which  was 
supposed  to  result  from  an  absorbed  and  exclusive 
contemplation  of  antiquity.  Engineering  and  technical 
schools  were  founded  as  separate  institutions,  in  response 
to  the  public  demand  for  trained  engineers.  The 
students  who  were  going  to  these  schools  required  a 
somewhat  different  preparation  than  did  those  going 
to  college  ;  so  the  high  schools  were  called  upon  to 
expand  in  this  direction  also. 

Finally,  the  colleges  themselves,  inspired  by  the  foun- 
dation of  Johns  Hopkins  University,  began  to  develop 
graduate  schools,  and  to  expand  into  universities. 


8  THE  TEACHING  OF  PHYSICS 

Graduates  of  American  colleges  began  to  appear  in  large 
numbers  as  students  in  foreign  universities.  These 
men  returned  filled  with  the  spirit  of  research,  and 
became  a  source  of  inspiration  to  college  faculties  and 
students  alike.  A  great  wave  of  enthusiasm  for  origi- 
nal investigation  and  the  extension  of  the  boundaries 
of  knowledge  swept  over  the  country,  completely  swamp- 
ing the  older  ideas  of  the  teaching  functions  of  the 
colleges.  This  wave  is  still  upon  us,  but  there  are 
evidences  that  its  force  is  spent,  and  that  it  is  beginning 
to  subside. 

This  wave  of  enthusiasm  for  research  affected  the 
high  schools,  too,  in  a  marked  way.  Teachers  came 
to  the  schools  from  the  colleges  filled  with  the  intoxica- 
tion of  it.  Ideas  of  accurate  measurement,  rigor,  and  fo 
logical  form  were  carried  into  the  school  work  with  an 
eagerness  on  the  part  of  the  teachers  which  was  only 
equaled  by  the  indifference  with  which  the  pupils 
received  them.  Nevertheless,  no  one  can  deny  that 
much  good  has  come  to  the  schools  from  this  whole 
movement.  Some  of  the  effects  of  it  as  they  appeared 
in  the  work  in  physics  will  be  considered  in  a  later 
chapter. 

Under  the  circumstances,  it  is  not  surprising  that  the 
high  schools  "  gravitated  toward  the  colleges."  More- 
over, the  elementary  schools  were  also  undergoing  such 


THE  BACKGROUND  9 

rapid  changes  that  superintendents  of  public  instruction 
were  absorbed  in  the  work  of  their  reorganization. 
The  kindergarten  ideas  that  were  "  made  in  Germany," 
the  Quincy  Movement  under  Colonel  Parker,  the 
doctrine  of  "  interest,"  the  findings  of  "  paidology " 
were  all  clamoring  for  recognition.  Under  this  stress 
of  conflicting  ideas,  the  high  schools  were  more  or  less 
left  by  their  legal  guardians  to  shift  for  themselves. 
The  dominant  idea  of  the  times  was  that  education  was 
preparation  for  life;  and  since  preparation  for  college 
was  regarded  as  the  best  possible  preparation  for  life, 
education  was  preparation  for  college.  Therefore  the 
high  schools,  left  without  the  paternal  care  that  might 
have  kept  alive  the  family  ties  which  bound  them  to 
the  lower  grades  of  public  schooling,  naturally  turned 
to  the  college  as  their  guide,  philosopher,  and  friend. 

4.  The  Committee  of  Ten.  —  The  stress  and  struggle 
of  the  conflicting  ideas  that  have  just  been  mentioned 
soon  produced  a  sort  of  chaos  that  was  intolerable.  This 
condition  led  the  National  Educational  Association, 
in  1892,  to  appoint  its  well-known  Committee  of  Ten. 
The  preliminary  investigations  of  this  committee  brought 
out  the  facts  that  in  forty  schools,  selected  as  typical: 
first,  the  total  number  of  different  subjects  taught 
was  nearly  forty ;  second,  that  many  of  these  subjects 
were  taught  for  such  short  periods  that  little  train- 


10  THE  TEACHING  OF  PHYSICS 

ing  could  be  derived  from  them;  and  third,  that  the 
time  allotted  to  the  same  subject  in  different  schools 
differed  widely.  1 

The  general  educational  principles  advocated  in  the 
report  of  this  committee  are  too  well  known  and  too 
generally  accepted  to  need  be  more  than  mentioned  here. 
Since  the  publication  of  the  report,  schools  have  been  and 
still  are  trying  to  correlate  studies  into  well-knit  curricula, 
to  secure  better  trained  teachers,  to  abolish  short  informa- 
tional courses,  to  develop  consecutive  and  more  extensive 
courses,  and  to  compel  pupils  to  divide  their  work  among 
what  the  committee  called  the  "  four  principal  fields 
of  knowledge,"  —  languages,  mathematics,  history,  and 
natural  science.  In  these  matters  there  can  be  no  doubt 
that  the  influence  of  this  report  has  been  widespread  and 
effective. 

The  influence  of  this  report  on  the  simplification  and 
standardization  of  school  administration  has  also  been 
excellent.  The  committee  adopts  "  the  number  four  as 
the  standard  number  of  weekly  periods"  which  "will 
not  make  it  impossible  to  carry  into  effect  the  funda- 
mental conception  of  all  the  Conferences ;  namely,  — 
that  all  the  subjects  .  .  .  should  be  taught  consecutively 
enough  and  extensively  enough  to  make  every  subject 

1  Report  of  the  Committee  of  Ten  of  the  National  Educational  Asso- 
ciation. American  Book  Co.,  1894,  pp.  3  sq. 


THE  BACKGROUND  II 

yield  that  training  which  it  is  best  fitted  to  yield."1 
This  will  readily  be  recognized  as  the  beginning  of  the 
"  unit "  system  which  is  now  the  basis  of  high-school 
administration  and  of  the  evaluation  of  high-school  work 
for  purposes  of  college  entrance.  All  of  this  is  too  familiar 
to  make  a  detailed  discussion  of  it  necessary  in  this 
brief  sketch. 

There  are  two  points  in  the  report  whose  implications 
have  not  been  generally  understood,  but  which  are  of 
importance  for  the  further  discussion  of  the  teaching 
problem.  In  the  first  place,  the  report  states  (p.  16): 
"  On  one  very  important  question  of  general  policy, 
which  affects  profoundly  the  preparation  of  all  school 
programs,  the  Committee  of  Ten  and  all  the  Con- 
ferences are  absolutely  unanimous.  Among  the  questions 
suggested  for  discussion  in  each  Conference  was  the 
following :  — 

"7.  Should  the  subject  be  treated  differently  for 
pupils  who  are  going  to  college,  for  those  who  are  going 
to  a  scientific  school,  and  for  those  who,  presumably, 
are  going  to  neither  ? 

"This  question  is  answered  unanimously  in  the  negative 

by  all  the  Conferences,  .  .  .  and  the  Committee  of  Ten 

unanimously  agree  with  the  Conferences.     Ninety-eight 

teachers,   intimately   connected   either   with   the  work 

1  Report  of  the  Committee  of  Ten,  p.  41. 


12  THE  TEACHING  OF  PHYSICS 

of  American  secondary  schools,  or  with  the  results 
of  that  work  as  they  appear  in  students  who  come  to 
college,  unanimously  declare  that  every  subject  that 
is  taught  at  all  in  a  secondary  school  should  be  taught 
in  the  same  way  and  to  the  same  extent  to  every 
pupil  so  long  as  he  pursues  it,  no  matter  what  the 
probable  destination  of  the  pupil  may  be,  or  at  what 
point  his  education  is  to  cease." 

Again  (p.  51):  "  The  secondary  schools  of  the  United 
States,  taken  as  a  whole,  do  not  exist  for  the  purpose  of 
preparing  boys  and  girls  for  colleges.  ...  A  secondary 
school  program  intended  for  national  use  must  there- 
fore be  made  for  those  children  whose  education  is  not 
to  be  pursued  beyond  the  secondary  school." 

In  these  two  passages  we  have  defined  the  general  point 
of  view  of  the  committee;  namely,  preparation  for  life 
is  preparation  for  college.  In  the  light  of  this  statement 
it  is  easy  to  understand  why  the  committee  organized 
only  nine  conferences,  one  for  "  each  principal  subject 
which  enters  into  the  programs  of  secondary  schools 
and  into  the  requirements  for  admission  to  college." 
It  is  also  easy  to  see  why  "  the  list  of  subjects  which 
the  conferences  deal  with  as  proper  for  secondary 
schools  is  as  follows :  (i)  languages,  Latin,  Greek, 
English,  German,  French ;  (2)  mathematics,  algebra, 
geometry,  and  trigonometry;  (3)  general  history  and 


THE  BACKGROUND  13 

the  intensive  study  of  special  epochs;  (4)  natural 
history,  including  descriptive  astronomy,  meteorology, 
botany,  zoology,  physiology,  geology,  and  ethnology, 
most  of  which  subjects  may  be  conveniently  grouped 
under  the  title  of  physical  geography;  and  (5)  physics 
and  chemistry.  The  Committee  of  Ten  assent  to  this 
list,  both  for  what  it  includes  and  for  what  it  excludes, 
with  some  practical  qualifications  to  be  mentioned 
below."  1 

It  seems  strange  that  the  list  of  subjects  which  the 
Conferences  considered  "  proper  for  secondary  schools  " 
should  coincide  with  the  list  of  subjects  required  for 
admission  to  college,  unless  we  recognize  that  the 
real  point  of  view  of  the  committee,  —  subconscious 
and  unquestioned,  —  was  that  preparation  for  college 
was  the  best  possible  preparation  for  life  for  everybody, 
whether  they  went  to  college  or  not.  This  idea  seems 
to  have  been  so  woven  into  the  warp  and  woof  of  educa- 
tional thinking  at  that  time,  that  its  color  and  its  fra- 
grance pervaded  every  garment  in  which  that  thinking 
clothed  itself. 

The  keynote  of  this  type  of  educational  thought  can 

be  found  in  many  places  in  the  report.     For  example, 

on  page  44  we  read :   "All  four  programs   (suggested 

by  the  committee)  conform  to  the  general  recommenda- 

1  Report  of  the  Committee  of  Ten,  p.  36. 


14  THE  TEACHING  OF  PHYSICS 

tions  of  the  Conferences ;  that  is,  they  give  time  enough 
to  each  subject  to  win  from  it  the  kind  of  mental  training 
it  is  fitted  to  supply,"  etc.  The  subconscious  back- 
ground is  thus  the  doctrine  of  formal  discipline  in  the 
form  which  states  that  discipline  and  educational  value 
depend  largely  on  the  subject  matter,  and  are  inherent 
in  a  preeminent  degree  in  those  subjects  which  the 
Conferences  considered  to  be  "proper  for  secondary 
schools." 

5.  The  Committee  on  College  Entrance  Require- 
ments. —  The  same  subconscious  background  may 
be  discerned  even  more  clearly  in  the  next  great  step 
forward  in  the  development  of  the  secondary  schools; 
namely,  in  the  Report  of  the  Committee  on  College 
Entrance  Requirements,  which  was  presented  to  the 
National  Educational  Association  in  1899.  The  im- 
mediate cause  of  the  appointment  of  this  committee  was 
the  reading  of  a  paper  by  Professor  William  Carey 
Jones,  of  the  University  of  California,  before  the  Depart- 
ment of  Secondary  Education  of  the  National  Educa- 
tional Association  at  its  meeting  in  Denver  in  1895. 
The  title  of  this  paper  was  The  Prospects  of  a  Federal 
Educational  Union.  The  ideas  which  Professor  Jones 
defended  were  these :  *  "I  plead,  in  behalf  of  the 
systematization  of  our  state  school  work,  (i)  for  the 

1  N.  E.  A.  Reports,  1895,  P-  597- 


THE  BACKGROUND  15 

adoption  of  an  effective,  thorough,  well-guarded  scheme 
of  accrediting,  where  none  now  exists;  (2)  for  the 
strengthening  and  safeguarding  of  existing  accrediting 
schemes;  (3)  for  the  abandonment  of  all  certificating 
of  schools  by  colleges  and  universities,  whether  open 
and  above  board  or  sub  rosa,  without  inspection  of  the 
actual  work  of  the  school.  .  .  .  Finally,  I  wish  to  rec- 
ommend that  a  committee  ...  be  organized  to  devise 
plans  for  carrying  out  such  suggestions  as  I  have  made, 
or  for  otherwise  promoting  a  federation  of  our  educa- 
tional institutions." 

"  Discussion  of  these  theses  led  to  a  motion  for  the 
appointment  of  a  committee  to  report  a  plan  of  action 
on  the  basis  of  Professor  Jones's  paper.  This  committee 
presented  the  following  report :  *  — 

"  WHEREAS,  The  most  pressing  need  for  higher  edu- 
cation in  this  country  is  a  better  understanding  between 
the  secondary  schools  and  the  colleges  and  universities 
in  regard  to  requirement  for  admission;  therefore 

"Resolved,  That  the  Department  of  Secondary  Edu- 
cation appoint  a  committee  of  five,  and  request  the 
appointment  of  a  similar  committee  by  the  Department 
of  Higher  Education,  the  two  to  compose  a  committee  of 
conference,  whose  duty  it  shall  be  to  report  at  the 
next  annual  meeting  a  plan  for  the  accomplishment 

1  Report  of  the  Committee  on  College  Entrance  Requirements,  p.  5. 


1 6  THE  TEACHING  OF  PHYSICS 

of  this  end,  so  urgently  demanded  by  the  interests  of 
higher  education." 

The  committee  thus  constituted  began  work  in  1896. 
The  first  item  in  its  plan  of  work  is  this  (Report,  p.  9) :  — • 

"  i.  The  committee  should  invite  the  active  coopera- 
tion of  associations  already  organized  for  the  study  of 
such  problems;  it  should  appoint  representative  sub- 
committees of  specialists  interested  in  the  various 
subjects, —  all  with  a  view  to  the  ultimate  determina- 
tion of  what  should  constitute  a  normal  requirement  in 
each  of  the  subjects  set  for  admission  to  college." 

Accordingly,  nine  subcommittees  were  organized,  one 
for  each  of  the  subjects  "  set  for  admission  to  college  "  ; 
namely,  classical  languages,  modern  languages,  history, 
mathematics,  physical  geography,  chemistry,  botany, 
zoology,  and  physics.  It  will  be  noted  that  none  of  the 
technical  subjects,  like  drawing,  shop  work,  domestic 
science,  stenography,  etc.,  appear  in  this  list. 

The  general  committee  summed  up  its  conclusions  in 
fourteen  resolutions.  All  of  these  are  worthy  of  careful 
study;  but  two  of  them  are  of  particular  importance 
for  the  present  discussion.  The  first  of  these  is  (Report, 

p.  38):- 

"  XII.  Resolved,  That  we  recommend  that  any  piece 
of  work  comprehended  within  the  studies  included  in  this 
report  that  has  covered  at  least  one  year  of  four  periods 


THE  BACKGROUND  17 

a  week  in  a  well-equipped  secondary  school,  under  com- 
petent instruction,  should  be  considered  worthy  to  count 
toward  admission  to  college." 

The  italics  indicate  what  has  been  shown  by  the  sub- 
sequent development  to  have  been  the  important  point 
in  this  resolution.  They  indicate  the  supremacy  of  the 
belief  that  discipline  and  culture  are  inherent  in  certain 
kinds  of  subject  matter,  and  are  not  dependent  upon 
the  reaction  of  the  pupils  to  that  subject  matter. 

The  other  important  resolution  of  the  general  com- 
mittee is  this  (Report,  p.  30) :  — 

"  II.  Resolved,  That  the  teachers  in  the  secondary   * 
schools  should  be  college  graduates,  or  have  the  equiva- 
lent of  a  college  education." 

The  high  schools  have  tried  to  put  this  resolution  into 
effect  with  good  success.  At  present  most  of  the  teachers 
in  the  high  schools  are  college  graduates.  This  is  un- 
doubtedly a  mark  of  excellent  progress.  It  has  not, 
however,  been  successful  in  every  way;  for  college 
graduates  have  too  often  proved  to  be  poor  teachers,  j 
notwithstanding  the  fact  that  they  were  good  scholars.  > 
The  secondary  schoolmen  are  desperately  familiar  now 
with  the  actual  results  of  the  combined  operation  of 
these  two  resolutions.  These  effects,  as  far  as  physics 
is  concerned,  will  be  discussed  in  detail  in  a  subsequent 
chapter. 


1 8  THE  TEACHING  OF  PHYSICS 

Two  other  points  about  this  report  are  significant  of 
the  school  conditions  at  the  time  of  its  publication. 
The  first  is  that  the  various  sections  of  the  report  are 
signed  by  seventy-two  college  men,  eleven  high-school 
principals,  and  twenty-three  high-school  teachers. 

The  other  is  thus  expressed  in  the  report  (p.  43): 
"  Acting  on  these  lines,  the  committee  has  devoted 
its  chief  energies,  through  several  years,  to  securing  the 
formulation  of  satisfactory  courses  of  study  which 
should  serve  as  units,  or  norms,  worthy  of  national 
acceptance.  .  .  .  These  courses  of  study  constitute  so 
many  national  norms,  or  units,  out  of  which  any  school 
may  make  up  as  rich  a  program  of  studies  as  its  means 
and  facilities  permit."  It  will  be  noted  that  the  idea  of 
national  uniformity  of  school  work,  and  the  notion  of 
measuring  that  work  by  "units/'  here  find  their  full 
expression. 

This  report  of  the  Committee  on  College  Entrance 
Requirements  marks  the  culmination  of  the  supremacy 
of  the  ideas  on  which  it  is  based,  —  the  doctrine  of  formal 
discipline  and  that  of  preparation  for  college  being  the 
best  preparation  for  life.  Since  then,  these  two  educa- 
tional hypotheses  have  been  declining  in  influence. 
Their  weakness  lay  in  the  fact  that  they  failed  to  take 
account  of  the  emotional  reaction  of  the  pupils  to  the 
work  and  of  the  value  of  vocational  aims  in  securing 


THE  BACKGROUND  19 

vital  work.  They  have  now  been  superseded  by  the 
theory  of  motivation  and  the  idea  that  education  is 
neither  preparation  for  college  nor  preparation  for  life, 
but  life  itself. 

During  the  period  of  transition  from  one  set  of  educa- 
tional theories  to  the  other,  the  public  high  schools  have 
continued  to  grow  in  a  marvelous  way.  There  are  several 
additional  points  about  them  that  need  to  be  noted  in 
order  to  make  clear  the  present  conditions  which  form 
the  background  of  the  problem  of  physics  teaching. 

6.  The  Predominance  of  Small  High  Schools.  —  In 
the  first  place,  the  curricula  and  syllabi  that  have  been 
issued,  like  those  in  the  reports  just  considered,  have 
generally  been  framed  by  college  men  and  principals 
and  teachers  from  the  large  high  schools,  with  the  needs 
and  possibilities  of  those  schools  in  mind.  Those  who 
have  framed  these  courses  seem  to  have  been  oblivious 
to  the  actual  conditions,  which  are  these : l  In  1910 
there  were  838  public  high  schools  in  cities  of  8000  popula- 
tion and  over.  These  schools  averaged  nineteen  teachers 
to  a  school,  twenty-seven  pupils  to  a  teacher,  and  516 
pupils  to  a  school.  The  total  number  of  pupils  in  these 
large  schools  are  432,643.  This  is  47.3  per  cent  of  the 
total  number  of  pupils  (915,061)  in  all  the  public  high 
schools  in  the  country. 

1  U.  S.  Bureau  of  Education,  Report  for  1910,  II,  p.  1131. 


20  THE  TEACHING  OF  PHYSICS 

In  the  cities  of  less  than  8000  population,  there  were 
9375  public  high  schools.  These  small  schools  averaged 
about  three  teachers  to  a  school,  nineteen  pupils  to  a 
teacher,  and  fifty-two  pupils  to  a  school.  The  total 
number  of  pupils  in  these  schools  was  482,418,  or  50,000 
more  than  were  enrolled  in  the  large  schools.  This  is 
52.7  per  cent  of  the  total  number  of  pupils  in  all  public 
high  schools. 

A  moment's  consideration  will  convince  any  one  that 
the  vast  majority  of  the  pupils  in  these  small  schools, 
which  are  located  in  rural  and  manufacturing  communi- 
ties and  which  contain  more  than  half  the  high-school 
population,  cannot  be  nourished  on  a  diet  of  Latin, 
French,  German,  algebra,  geometry,  and  the  rest  of 
the  subjects  declared  by  the  Committee  of  Ten  to  be 
"  proper  for  secondary  schools."  These  subjects  are 
foreign  to  the  lives  of  most  of  the  members  of  these 
communities,  and  hence  schooling  in  these  subjects  can- 
not be  education  for  them,  since  education  is  life. 

On  the  other  hand,  college  men  know  very  well  that 
some  of  the  best  students  in  college  come  from  these 
small  schools ;  and  the  public  at  large  must  recognize 
the  fact  that  many  of  the  most  noted  and  useful  of  our 
citizens  are  reared  in  these  same  smaller  communities. 

It  is  also  clear  that  only  the  largest  schools  —  schools 
with  say  twenty  or  more  teachers  —  can  support  a  teacher 


THE  BACKGROUND  21 

who  is  a  specialist  in  any  subject  like  physics  and  who 
teaches  nothing  else.  It  is  safe  to  say  that  in  the  10,213 
public  high  schools  in  the  country  there  are  not  more  than 
300  teachers  who  teach  nothing  but  physics,  while  10,000 
of  those  who  teach  physics  in  high  schools  must  also 
teach  one  or  more  other  subjects.  Hence  the  college 
demand  for  a  kind  of  physics  that  can  be  taught  well 
only  by  a  specialist  in  physics  is  unreasonable.  It  is 
a  demand  that  cannot  be  adequately  met  in  more  than 
one  out  of  every  thirty-three  schools  in  the  country. 

7.  Elimination  from  High  Schools.  —  In  the  second 
place,  there  is  a  great  " mortality"  in  the  high  schools. 
In  1910,  there  were  392,505  pupils  in  the  first  year  class, 
247,936  in  the  second,  163,176  in  the  third,  and  111,444 
in  the  fourth.  Of  those  in  the  fourth  class,  111,363 
graduated,  and  of  these,  37,811  were  prepared  for  college. 
In  order  to  obtain  accurate  comparisons,  we  should,  of 
course,  compare  the  number  of  graduates  in  1910  with 
the  number  that  entered  four  years  before.  Since  this 
number  is  not  on  record,  we  compare  the  number  of 
graduates  with  the  number  that  entered  in  1907,  which 
was  333>274-  It  thus  appears  that  about  one  third  of 
those  who  entered  survived  to  graduate;  and  of  these 
survivors,  but  one  third  were  prepared  for  college. 
Hence,  only  about  one  ninth  of  those  who  enter  the 
public  high  schools  come  through  prepared  for  college. 


22  THE  TEACHING  OF  PHYSICS 

This  elimination  of  pupils  from  the  public  high  schools 
has  been  the  subject  of  much  study  of  late.  Prominent 
among  these  studies  is  the  investigation  by  the  Mas- 
sachusetts Commission  on  Industrial  and  Technical 
Education,  appointed  by  the  governor  in  1904.  This 
report  revealed  the  fact  that  there  were  some  25,000 
children  in  the  commonwealth  of  Massachusetts  who  were 
between  the  ages  of  fourteen  and  sixteen  but  who  were 
not  enrolled  in  either  the  public  or  the  private  schools, 
and  who  were  either  not  in  any  gainful  occupation,  or 
were  employed  at  the  lowest  class  of  unskilled  labor, 
commanding  a  very  low  rate  of  wages,  with  little  or 
no  prospect  of  advancement. 

This  report  led  to  the  appointment  of  a  state  com- 
mission to  establish  industrial  schools  in  the  state. 
Several  schools  of  this  type,  like  the  one  at  New  Bedford, 
have  been  established  independent  of  the  public  high 
schools,  whose  functions  they  thus  in  part  assume.  The 
establishment  of  these  schools  as  separate  schools, 
instead  of  introducing  the  industrial  work  into  the  public 
high  schools,  was  due  to  the  fact  that  the  high  schools 
were  regarded  by  the  commission  as  too  conservative, 
and  too  much  given  over  to  teaching  only  subjects  con- 
sidered "  proper  for  secondary  schools,"  to  make  it 
possible  to  have  them  introduce  the  new  kind  of  work 
promptly  and  successfully. 


THE  BACKGROUND  23 

8.  Recent  Tendencies.  —  The  response  of  the  high 
schools  to  the  present  demand  for  work  that  shall  be 
significant  both  to  the  pupils  and  to  the  communities 
that  support  the  schools  is,  however,  making  itself 
heard  in  such  cases  as  the  new  technical  high  school  in 
Cleveland,  the  two-year  industrial  courses  in  the  high 
schools  of  Chicago,  the  experiments  at  Fitchburg,  Mass., 
and  those  at  Cincinnati.  New  ideas  and  a  new  enthusiasm 
are  thus  beginning  to  take  hold  of  the  public  high  schools, 
and  they  now  seem  to  have  awakened  to  the  greatness 
of  their  problem  of  democratic  education,  and  to  have 
undertaken  experiments  which  will  gradually  contribute 
to  its  solution. 

This  awakening  of  the  high  schools  to  their  oppor- 
tunities and  their  obligations  amounts  to  a  complete 
abandonment  of  the  traditions  of  following  college 
entrance  requirements.  What  the  colleges  will  do  to 
contribute  their  full  share  to  the  progress  now  being 
made  by  the  schools  remains  to  be  seen.  Harvard 
has  this  year  adopted  a  new  set  of  entrance  requirements, 
in  which,  however,  she  clings  closely  to  the  demand  for 
none  but  those  subjects  which  the  Committee  of  Ten 
considered  "  proper  for  secondary  schools." 1  The 
University  of  Chicago  has  also  adopted  a  new  set  of 

1  Science,  Vol.  33,  pp.  182,  793;  Educational  Review,  Vol.  42,  p.  71, 
June,  1911. 


24  THE  TEACHING  OF  PHYSICS 

requirements,  which  allow  one  third  of  the  pupil's  time 
in  the  high  school  to  have  been  spent  on  any  kind  of 
work  for  which  the  high  school  itself  gives  credit  toward 
its  own  graduation.1  A  committee  of  the  Department  of 
Secondary  Education  made  a  valuable  report  on  this 
subject,  and  the  National  Council  of  Education  devoted 
one  session  to  its  discussion  at  the  meeting  of  the  National 
Educational  Association  at  San  Francisco  in  ipn.2 
There  are  many  other  signs  of  activity  on  this  subject, 
and  many  omens  which  portend  greater  freedom  for 
both  schools  and  colleges,  and  the  gradual  closing  up 
of  the  chasm  that  still  yawns  too  widely  between  present- 
day  schooling  and  that  education  which  is  life. 

^     l  Science,  Vol.  33,  p.  945,  June  23,  191 1 ;  Educational  Review,  Vol.  42, 
p.  186,  September,  1911. 
8  N.  E.  A.  Reports,  1911. 


CHAPTER  II 

NATURAL  PHILOSOPHY 

9.  University   Physics.  —  Physics   has   been   one   of 

the  subjects  of  study  in  the  European  Universities 
almost  from  their  foundation.  The  scientist  of  to-day, 
however,  would  be  loth  to  recognize  the  courses  that 
were  given  then  under  that  name  as  courses  in  what  is 
now  called  physics.  For  these  Middle- Age  studies  of 
physics  consisted  in  memorizing  Aristotle's  speculations 
on  this  subject,  and  in  having  hair-splitting  disputa- 
tions as  to  their  meanings  and  their  possible  implications. 

This  sort  of  physics  continued  to  hold  a  place  in  the 
university  curriculum  as  long  as  Aristotle  was  the  idol 
and  sole  authority  of  those  schools.  True,  we  find 
Roger  Bacon  objecting  to  this  practice  as  early  as  I276,1 
but  his  polemics  against  this  sort  of  "  science  "  and  his 
suggestions  for  something  better  fell  on  deaf  ears.  The 
changes  which  he  advocated  did  not  come  about  until 
some  three  centuries  had  rolled  by.  The  end  of  the 
sixteenth  century  marks  the  time  of  the  awakening  to 

1  Roger  Bacon,  Opus  Majus,  Edition  Jebb,  London,  1733,  Preface. 

25 


26  THE  TEACHING   OF  PHYSICS 

the  new  point  of  view,  which  has  remained  characteristic 
of  the  development  of  physics  into  its  present  form. 
From  the  time  of  Galileo  (1564-1643),  the  growth  of 
modern  physics  has  been  continuous  and  closely  inter- 
woven with  the  development  of  mathematics.  This 
development  has  determined  the  nature  of  the  physics 
instruction  in  college  and  university  courses. 

The  fundamental  ideas  that  have  characterized  this 
development  of  university  courses  in  physics  have  re- 
cently been  analyzed  and  explained  with  great  clearness 
by  Bouasse  and  Duhem.1  Bouasse  shows  that  the  science 
of  physics  has  always  tried  to  "  explain  "  phenomena ; 
by  which  is  meant  "  simply  and  solely  to  bring  each  fact 
under  some  form."  2  Thus  the  phenomena  of  refraction 
are  "  explained  "  when  it  has  been  shown  that  the  facts 
of  refraction  can  be  correctly  resumed  under  the  form, 
sin  i  =  n  sin  r.  The  progress  of  the  science  of  physics 
has  then  been  effected  by  first  establishing  these  forms, 
and  then  deducing  their  consequences,  discovering  their 
interrelations,  and  resuming  the  less  general  under  the 
more  general.  For  example,  the  form  just  given  was  first 
established  from  a  study  of  the  facts  of  refraction,  and 
then  later  shown  to  be  a  special  case  of  the  principle  of 

1 H.  Bouasse,  De  la  Methode  des  Sciences,  Paris,  Alcan,  1909, 
pp.  73-110.  Duhem,  La  Theorie  Physique,  son  Object  ct  sa  Structure, 
Paris,  Chevalier  et  Reviere,  1906.  2  Bouasse,  I.e.,  p.  91. 


NATURAL  PHILOSOPHY  27 

least  action.  In  this  process,  the  interest  of  the  modern 
scientist  centers  on  the  second  part,  namely,  the  deduc- 
tion of  consequences,  and  the  resumption  of  the  less 
general  under  the  more  general  forms. 

It  is  because  this  ^university  physics  has  now  come  to 
be  essentially  a  study  of  forms  that  it  is  so  closely  allied 
to  mathematics.  Indeed  all  physicists  well  know  how 
their  science  has  often  been  retarded  in  its  progress  be- 
cause the  mathematics  required  had  not  yet  been  worked 
out.  Poincare  recognizes  this  fact  when  he  shows  that 
a  law  of  physics  is  nothing  but  a  differential  equation  — 
a  mathematical  form ; 1  or  when  he  calls  the  m  in  the 
form  /  =  ma,  a  "  coefficient  in  the  equation."  2  This 
matter  will  be  considered  more  in  detail  in  a  later  chap- 
ter; here  it  is  important  to  note  that  this  "pure  "  phys- 
ics, which  has  developed  in  the  universities,  and  which 
is  responsible  for  the  growth  of  the  science,  consists  es- 
sentially in  a  study  of  mathematical  forms.  It  postu- 
lates the  accepted  forms,  and  then  spends  its  energies  in 
deducing  their  consequences  and  tracing  their  implica- 
tions. 

This  university  science  of  physics  owes  its  growth  and 
its  vitality  to  the  fact  that  some  of  the  world's  greatest 
geniuses  have  seen  in  the  problem  of  establishing  suitable 

1  Poincare,  Science  and  Hypothesis,  p.  173,  New  York,  The  Science 
Press,  1905.  2  Poincare",  I.e.,  p.  76. 


28  THE  TEACHING  OF  PHYSICS 

forms  and  tracing  their  consequences  a  problem  full  of 
significance  and  one  worthy  of  their  utmost  efforts.  It 
now  stands,  in  its  present  highly  developed  form,  as  a 
monument  to  one  of  the  finest  traits  of  human  character, 
—  the  disinterested  devotion  of  one's  self  completely  to 
the  accomplishment  of  a  significant  task. 

10.  Natural  Philosophy.  —  Physics  in  the  schools  is 
not  so  old  as  physics  in  the  universities.  It  is  impossible 
to  state  just  when  it  was  introduced  into  school  curricula, 
but  there  is  record  of  its  having  been  taught  in  the 
academy  at  Northampton,  England,  as  early  as  1729.* 
There  were  numerous  books  on  natural  philosophy  in- 
tended for  school  use  published  during  the  eighteenth 
century.  One  of  the  most  interesting  of  these  is  that  of 
James  Ferguson,  which  was  published  about  1750.  This 
book  passed  through  many  editions,  was  revised  in  1805 
by  Sir  David  Brewster,  and  brought  out  in  America  in 
1806  by  Robert  Patterson,  Professor  of  Natural  Phi- 
losophy in  the  University  of  Pennsylvania.  Mr.  Fer- 
guson was  a  self-educated  man,  a  mechanic  by  trade,  but 
was  elected  a  member  of  the  Royal  Society  of  London, 
because  of  his  ability  of  making  abstract  philosophical 
subjects  clear. 

In  his  introduction  to  this  book  of  Ferguson's,  Sir 
David  Brewster  says :  "  The  chief  object  of  Mr.  Fer- 

1  Brown,  Making  of  Our  Middle  Schools,  p.  171. 


NATURAL  PHILOSOPHY  29 

guson's  labors  was  to  give  a  familiar  view  of  physical 
science  and  to  render  it  accessible  to  those  who  are 
not  accustomed  to  mathematical  investigation.  To  his 
labors  we  must  attribute  that  general  diffusion  of  scien- 
tific knowledge  among  the  practical  mechanics  of  this 
country,  which  has,  in  a  great  measure,  banished  those 
antiquated  prejudices  and  erroneous  maxims  of  construc- 
tion that  perpetually  mislead  the  unlettered  artist."  1 

In  America,  Natural  Philosophy  was  one  of  the  sub- 
jects studied  in  the  academies  from  their  beginning.  In 
1754,  we  find  Rev.  Wm.  Smith  teaching  "  natural  and 
moral  philosophy  "  at  the  "  Publick  Academy  in  the  City 
of  Philadelphia, "  2  the  one  founded  under  the  influence 
of  Benjamin  Franklin.  It  was  part  of  the  curriculum  of 
the  first  public  high  school,  the  English  High  in  Boston, 
from  the  start  in  1821.  It  also  appears  in  the  courses  of 
study  in  the  first  public  high  schools  in  New  York  in 
1825.3 

This  early  introduction  of  natural  philosophy  into  the 
courses  of  the  academies  and  the  public  high  schools 
shows  that  the  purpose  for  which  it  was  intended  was 
quite  different  from  that  which  supplied  the  motive  for 
the  university  physics.  The  academies  were  founded  in 

1  Woodhull,  The  Teaching  of  Physical  Science,  Teachers  College  Record, 
Vol.  XI,  No.  i,  p.  18,  January,  1910. 

s  Brown,  Making  of  Our  Middle  Schools,  p.  184,  *  Ibid.,  p.  307. 


30  THE  TEACHING  OF  PHYSICS 

order  that  the  pupils  might  learn  "  those  things  that  are 
likely  to  be  most  useful  and  most  ornamental,  regard 
being  had  to  the  several  professions  for  which  they  were 
intended."  1  In  like  manner,  the  public  high  schools 
were  established  because  "  no  one  of  the  colleges  fully 
answered  the  public  need  as  regards  higher  education ;  "  2 
and  because  "  the  commercial  activities  of  the  larger 
towns  called  for  a  different  kind  of  training  from  that 
offered  by  the  schools  designed  to  prepare  for  college."  3 
Since  natural  philosophy  was  taught  in  both  the  acad- 
emies and  the  public  high  schools  from  the  beginning, 
it  was  evidently  recognized  as  one  of  the  "  most  useful 
and  most  ornamental "  of  studies,  and  one  well  calcu- 
lated to  meet  the  needs  of  the  people  in  their  struggle 
for  the  common  good. 

But  since  the  colleges  did  not  recognize  this  subject 
as  one  fit  to  receive  credit  for  college  entrance  until  1872, 
it  appears  that  the  nature  of  the  instruction  in  natural 
philosophy  in  the  academies  and  high  schools  differed 
widely  from  that  demanded  by  the  contemporary  college 
ideas  of  education.  As  Benjamin  Franklin  remarked  in 
1783,  "the  Latinists  were  combined  to  decry  the  English 
schools  as  useless.  It  was  without  example,  they  said,  as 
indeed  they  still  say,  that  a  school  for  teaching  the  vulgar 

1  Ante,  p.  2.  2  Brown,  I.e.,  p.  280. 

8  Ibid.,  p.  295. 


NATURAL  PHILOSOPHY  31 

tongue  and  sciences  in  that  tongue  was  ever  joined 
with  a  college."  1 

1 1 .  Old  Texts  of  Natural  Philosophy.  —  While  opinions 
may  differ  as  to  whether  this  natural  philosophy  taught 
"  those  things  that  were  most  ornamental,"  all  must 
agree  that  it  taught  "  those  things  that  were  most  useful." 
Of  Ferguson's  book  Sir  David  Brewster  wrote,  in  1805 : 
"  No  book  upon  the  same  subject  has  been  so  generally 
read,  and  so  widely  circulated,  among  all  ranks  of  the 
community.  We  perceive  it  in  the  workshop  of  every 
mechanic.  We  find  it  transferred  into  the  different 
encyclopedias  which  this  country  has  produced,  and  we 
may  easily  trace  it  in  those  popular  systems  of  philosophy 
which  have  lately  appeared."  2 

An  inspection  of  the  contents  of  the  book  shows  us 
why  the  knowledge  it  contained  was  useful.  Sixty- two 
pages  are  devoted  to  machines,  and  forty  pages  to  pumps. 
When  we  recall  that  at  the  time  of  its  popularity  (1750- 
1825)  machinery  was  being  rapidly  introduced  into  all 
branches  of  industry,  and  that  this  was  the  age  of  the 
invention  of  the  steam  engine,  the  steamboat,  and  the 
locomotive,  we  may  understand  why  a  book  of  this  sort 
was  so  popular.  It  supplied  a  kind  of  information  for 
which  there  was  a  large  and  constantly  increasing  de- 

1  Brown,  I.e.,  p.  190. 

2  Woodhull,  Teaching  of  Physical  Science,  p.  18. 


32  THE  TEACHING  OF  PHYSICS 

mand.  An  age  of  machinery  and  invention,  an  era  of 
rapid  industrial  expansion,  was  developing,  and  the  clas- 
sics were  unable  to  meet  the  demand  for  information  on 
these  subjects  as  they  had  met  the  demand  for  knowledge 
of  secular  things  at  the  time  of  the  Renaissance.  A  new 
type  of  information  was  needed  and  demanded  by  the 
public;  and  natural  philosophy  and  the  other  sciences 
were  invoked  to  meet  the  need  and  supply  the  demand. 

That  the  natural  philosophy  of  those  days  satisfactorily 
met  the  public  demands  of  the  times  is  evidenced  by 
the  number  of  different  textbooks  that  were  published  on 
this  subject,  and  the  number  of  editions  through  which 
they  passed.  The  School  Compendium  of  Experimental 
Philosophy,  by  R.  G.  Parker,  published  in  1837,  ran 
through  twenty-two  editions  in  its  first  twelve  years. 
The  System  of  Natural  Philosophy,  by  J.  L>  Comstock, 
had  reached  its  seventy- third  edition  in  1846. 

The  title  pages  of  these  old  texts  bristle  with  such 
phrases  as  "The  principles  of  mechanics,  acoustics, 
optics,  are  familiarly  explained."  "  The  causes  of  many 
daily  occurring  natural  phenomena  are  familiarly  ex- 
plained." Their  authors  were  many-sided  men,  —  often 
clergymen.  Comstock  was  a  physician.  Besides  his 
Natural  Philosophy,  he  wrote  Introduction  to  Mineralogy, 
The  Elements  of  Chemistry,  Introduction  to  Botany,  Out- 
lines of  Geology,  Outlines  of  Physiology,  Natural  History 


NATURAL  PHILOSOPHY  33 

of  Birds,  etc.  Quackenbos  was  the  author  of  First  Les- 
sons in  Composition,  Illustrated  History  of  the  United 
States,  besides  having  written  his  Natural  Philosophy. 

The  prefaces  of  these  books  are  filled  with  statements 
like  these :  "  The  author  has  sought  to  render  a  subject, 
abstruse  in  some  of  its  connections,  easy  of  comprehen- 
sion, by  treating  it  in  a  clear  style,  taking  its  principles 
one  at  a  time  in  their  natural  order,  and  illustrating  them 
fully  with  the  facts  of  our  daily  experience  "  (Quacken- 
bos, 1859). 

"  It  has  been  the  chief  object  of  the  author  to  make 
himself  understood  by  those  who  know  nothing  of  mathe- 
matics, and  who  indeed  had  no  previous  knowledge  of 
natural  philosophy.  The  author  has  also  endeavored 
to  illustrate  the  subjects  as  much  as  possible  by  means 
of  common  occurrences,  or  common  things,  and  in  this 
manner  to  bring  philosophical  truths  as  much  as  practi- 
cable within  ordinary  requirements"  (Corns tock,  1846). 

"  The  author  has  explained  some  of  the  most  common 
and  interesting  phenomena  of  nature  in  a  manner  so 
familiar  and  simple,  that  even  young  children  cannot 
fail  to  understand  their  causes"  (Bakewell,  1833). 

These  few  from  a  multitude  of  similar  statements  show 
the  effort  that  was  made  to  bring  the  rapidly  increasing 
scientific  knowledge  of  the  times  home  to  young  people, 
without  trying  to  force  upon  them  that  study  of  mathe- 


34  THE  TEACHING  OF  PHYSICS 

matical  forms  and  their  interrelations  which  was  char- 
acteristic of  the  university  physics.  In  most  of  the 
natural  philosophies  that  were  published  prior  to  about 
1870,  you  will  search  in  vain  for  the  expression  of  prin- 
ciples in  algebraic  form.  The  diagrams,  too,  are  almost 
always  pictures  of  real  things,  —  real  pulleys,  with  a 
hand  pulling  the  rope ;  real  levers,  with  a  hand  pushing 
on  the  end.  The  geometrical  diagrams  of  simple  ma- 
chines, with  vectors  to  represent  the  forces,  were  prac- 
tically unknown. 

This  point  may  be  made  clearer  by  an  example.  In 
Corns tock,  1846  edition,  the  phenomena  of  falling  bodies 
is  treated  thus  (p.  26) :  — 

"85.  If  a  rock  is  rolled  from  a  steep  mountain,  its  '*' 
motion  is  at  first  slow  and  gentle,  but  as  it  proceeds 
downwards,  it  moves  with  perpetually  increased  velocity, 
seeming  to  gather  fresh  speed  every  moment,  until  its 
force  is  such  that  every  obstacle  is  overcome ;  trees  and 
rocks  are  beat  from  its  path,  and  its  motion  does  not 
cease  until  it  has  rolled  to  a  great  distance  on  the  plain." 


Velocity  of  Falling  Bodies 

11 86.  The  same  principle  of  increased  velocity  as 
bodies  descend  from  a  height,  is  curiously  illustrated  by 
pouring  molasses  or  thick  sirup  from  an  elevation  to  the 


NATURAL  PHILOSOPHY  35 

ground.  The  bulky  stream,  of  perhaps  two  inches  in 
diameter,  where  it  leaves  the  vessel,  as  it  descends,  is 
reduced  to  the  size  of  a  straw,  or  a  knitting  needle ;  but 
what  it  wants  in  bulk  is  made  up  in  velocity,  for  the  small 
stream  at  the  ground  will  fill  a  vessel  just  as  soon  as  the 
large  one  at  the  outlet. 

"  87.  For  the  same  reason,  a  man  may  leap  from  a 
chair  without  danger,  but  if  he  jumps  from  the  housetop, 
his  velocity  becomes  so  much  increased,  before  he  reaches 
the  ground,  as  to  endanger  his  life  by  the  blow.  It  is 
found  by  experiment,  that  the  motion  of  a  falling  body  is 
increased,  or  accelerated,  in  regular  mathematical  pro- 
portions. 

"  88.  These  increased  proportions  do  not  depend  on 
the  increased  weight  of  the  body,  because  it  approaches 
nearer  the  center  of  the  earth,  but  on  the  constant  opera- 
tion of  the  force  of  gravity,  which  perpetually  gives  new 
impulses  to  the  falling  body,  and  increases  its  velocity. 

"89.  It  has  been  ascertained  by  experiment,  that  a 
body,  falling  freely,  and  without  resistance,  passes 
through  a  distance  of  sixteen  feet  and  one  inch  during 
the  first  second  of  time.  Leaving  out  the  inch,  which  is 
not  necessary  for  our  present  purpose,  the  ratio  of  de- 
scent is  as  follows. 

"  90.  If  the  height  through  which  a  body  falls  in  one 
second  be  known,  the  height  which  it  falls  in  any 


36  THE  TEACHING  OF  PHYSICS 

proposed  time  may  be  computed.  For  since  the  height 
is  proportional  to  the  square  of  the  time,  the  height 
through  which  it  will  fall  in  two  seconds  will  be  four  times 
that  which  it  falls  through  in  one  second.  In  three  sec- 
onds it  will  fall  through  nine  times  that  space ;  in  four 
seconds  sixteen  times  that  of  the  first  second;  in  five 
seconds,  twenty-five  times,  and  so  on,  in  this  proportion." 
12.  Modern  High  School  Physics.  —  In  contrast  with 
this  sort  of  treatment,  consider  the  following  explanation 
of  the  same  subject  as  given  in  one  of  the  most  used  of 
the  modern  texts. 

"IV.      LAWS   OF   FALLING  BODIES 

"  60.  Uniform  Acceleration  applied  to  Falling  Bodies. 
—  Since  the  acceleration  g,  due  to  gravity,  is  constant 
for  small  distances  above  the  earth's  surface,  the  for- 
mulae already  obtained  for  uniformly  accelerated  motion 
may  be  directly  applied  to  falling  bodies.  The  relations 
between  velocity,  time,  space,  and  acceleration  are  ex- 
pressed by  the  equations  v  =  at  and  s  =  J  at2.  Sub- 
stituting g  for  a,  we  have 

1  =  0  (10) 

and  5  =  %  gt2.  (n) 

"  If  in  equation  (n)  /  is  made  one  second,  then  s  — 
J  g ;  or  the  space  described  in  the  first  second,  when  the 


NATURAL  PHILOSOPHY  37 

body  falls  from  rest,  is  half  the  value  of  the  acceleration 
of  gravity.  A  body  falls  490  cm.  the  first  second  ;  the 
velocity  attained  in  one  second  and  the  acceleration 
are  980  cm. 

"  To  find  the  space  passed  over  in  any  one  second,  find 
the  space  described  in  /  seconds,  and  in  (t  —  i)  seconds, 
and  subtract  the  latter  from  the  former.  Denoting  the 
distance  sought  by  5', 


The  distance  passed  over  in  any  second  is  equal  to  half 
the  product  of  g  and  one  less  than  double  the  number  of 
the  second.  By  combining  equations  (10)  and  (n)  we 

have  v*  =  2  gs.  (13) 

"61.  Laws.  —  The  laws  embodied  in  the  preceding 
formulae  may  be  expressed  as  follows  :  — 

I.  The  velocity  attained  by  a  falling  body  is  proportional 
to  the  time  of  falling. 

II.  The  space  described  is  proportional  to  the  square  of 
the  time. 

III.  The  acceleration  is  twice  the  space  through  which  a 
heavy  body  falls  in  the  first  second." 

The  former  of  these  quotations  is  a  good  sample  of  the 
descriptive  style  that  was  characteristic  of  these  natural 
philosophies,  and  the  second  shows  how  the  same  subject 


38  THE  TEACHING  OF  PHYSICS 

is  treated  at  present,  when  the  mathematical  forms  of 
the  university  physics  have  driven  out  the  more  tan- 
gible and  concrete  methods  of  the  older  books. 

The  educational  merits  of  this  change  will  be  discussed 
in  a  later  chapter.  Attention  is  drawn  to  it  here  for  the 
purpose  of  emphasizing  the  points:  i.  That  natural 
philosophy  was  introduced  into  the  schools  for  a  specific 
purpose,  namely,  to  supply  the  common  people  with  in- 
formation about  physical  phenomena  in  those  schools 
that  were  founded  for  the  common  good  and  supported 
by  the  public  funds.  2.  That  the  natural  philosophy, 
so  introduced  and  so  taught,  did^supply  the  desired  in- 
formation and  did  do  its  part  in  upbuilding  those  schools. 
3.  That  natural  philosophy  had  a  very  different  origin 
from  university  physics ;  since  the  latter  consists  essen- 
tially in  studying  mathematical^  forms,  in  discovering 
interrelations  among  these  forms,  and  in  deducing  and 
verifying  their  consequences. 

This  distinction  between  natural  philosophy  and  pure 
physics  —  this  recognition  of  the  fact  that  there  may  be 
a  fundamental  difference  between  pure  science  and  sci- 
ence in  the  service  of  education  —  has  been  clearly  rec- 
ognized by  some  authors  for  many  years.  Thus,  Neil 
Arnott's  Elements  of  Physics,  published  in  1826,  contains 
the  following :  "  Mathematics  are  at  present  generally 
made  the  beginning  of  the  study,  and  the  reason  assigned 


NATURAL  PHILOSOPHY  39 

is  that  scarcely  any  object  in  physics  can  be  described 
without  referring  to  quantity  or  proportion,  and  there- 
fore, without  using  mathematical  terms.  Now  this  is 
true ;  but  it  is  equally  true  that  the  mathematical  knowl- 
edge, acquired  by  every  individual  in  the  common  ex- 
perience of  childhood  and  early  youth,  is  sufficient  to 
enable  students  to  understand  all  the  great  laws  of  na- 
ture."1 

In  1847,  Jonn  W.  Draper,  in  his  Natural  Philosophy 
for  Schools,  says :  "  There  are  two  different  methods  in 
which  Natural  Philosophy  is  now  taught:  (i)  as  an  ex- 
perimental science;  (2)  as  a  branch  of  mathematics.  I 
believe  that  the  proper  course  is  to  teach  physical  science 
experimentally  first."  2 

Similar  statements  are  found  in  Hooker's  Natural 
Philosophy  for  Schools,  1863,  and  elsewhere.3  Recently 
a  reaction  against  the  study  of  mathematical  forms  under 
the  name  of  physics  has  taken  place,  and  physics  is  once 
more  coming  to  be  taught  as  an  experimental  and  in- 
formational science,  as  it  was  in  the  days  of  natural  phi- 
losophy. This  reaction  is  not  resurrecting  the  old  nat- 
ural philosophy,  with  all  its  acknowledged  faults  and 

1  Woodhull,  Teaching  of  Physical  Science,  Teachers  College  Record, 
Vol.  XI,  No.  i,  January,  1910,  p.  17. 

2  Woodhull,  l.c.,  p.  21. 

3  For  a  fuller  discussion  of  this  matter  the  reader  is  referred  to  Wood- 
hull,  I.e.,  pp.  1-82. 


40  THE  TEACHING  OF  PHYSICS 

shortcomings ;  it  is  leading  to  a  new  method  of  treating 
science  for  purposes  of  education.  It  is  hoped  that  the 
outlines  of  this  new  method,  and  the  principles  on  which 
it  is  based,  will  become  clearer  as  this  discussion  pro- 
gresses. 


CHAPTER  III 

,          PRESCRIBED  PHYSICS 

13.  Early  High  School  Physics.  —  Natural  philos- 
ophy disappeared  from  the  curricula  of  the  schools  about 
the  year  1872.  Its  place  has  since  then  been  occupied 
by  physics,  which  achieved  the  honor  of  recognition 
among  the  subjects  worthy  of  credit  for  entrance  to 
college  that  same  year.  It  was  at  this  time  that  the 
public  high  schools  began  their  rapid  growth  and  their 
equally  rapid  "gravitation  toward  the  colleges."  As 
has  already  been  rioted  (p.  20),  this  "  gravitation  "  con- 
tinued until  1899,  when  the  schools  struck  bottom  on 
the  Report  of  the  Committee  on  College  Entrance 
Requirements  and  rebounded  vigorously  upward. 

A  very  good  picture  of  the  condition  of  physics  in  the 
schools  during  the  early  years  of  this  period  is  given  in 
two  special  bulletins  issued  by  the  United  States  Bureau 
of  Education;  one  is  Bulletin  6,  1880,  compiled  by 
Frank  W.  Clarke,  Professor  of  Physics  at  the  University 
of  Cincinnati;  and  the  other  is  Bulletin  7,  1884,  com- 
piled by  Charles  K.  Wead,  Professor  of  Physics  at  the 
University  of  Michigan. 

41 


42  THE  TEACHING  OF  PHYSICS 

The  first  of  these  bulletins,  that  of  1880,  contains  a 
summary  of  the  replies  received  from  175  public  high 
schools  and  433  private  secondary  schools  to  a  question- 
naire issued  by  the  Bureau.  The  questions  called  for  in- 
formation as  to  the  time  of  introduction  of  the  course  in 
physics,  the  number  of  periods  a  week  devoted  to  it,  the 
text  used,  the  method  of  work,  the  amount  of  laboratory 
equipment,  the  amount  of  time  devoted  to  laboratory 
work,  whether  or  not  the  pupils  themselves  did  any 
laboratory  work,  and  whether  there  were  class  experi- 
ments by  the  teacher  or  not. 

From  the  tables  in  which  the  replies  are  summarized 
we  learn  that  there  were  at  that  time  but  four  secondary 
schools  in  the  country,  namely,  the  high  schools  at  Pitts- 
burgh and  Worcester,  the  Punchard  Free  School  at  An- 
dover,  and  the  Friends'  Select  School  at  Philadelphia, 
in  which  a  full  year's  work  in  physics  with  laboratory 
work  by  the  pupils  was  given.  Two  public  and  seven 
private  schools  reported  shorter  courses  with  laboratory 
work  by  the  pupils ;  thirty-eight  public  and  twelve  pri- 
vate schools  reported  a  full  year's  work  with  experi- 
ments by  the  teachers ;  fourteen  public  and  ninety-five 
private  schools  reported  one  year  or  less  of  textbook  work 
only ;  and  seven  public  and  six  private  schools  reported 
no  physics  at  all. 

The  most  popular  text  was  Steel's  Fourteen  Weeks  in 


PRESCRIBED  PHYSICS  43 

Physics,  which  was  used  in  thirty-four  public  and  one 
hundred  and  sixteen  private  schools ;  next  comes  Quack- 
enbos,  with  fifteen  public  and  seventy-one  private 
schools.  Norton's  Elements  of  Natural  Philosophy  was 
used  in  fifty-eight  schools ;  Wells  and  Cooley  in  thirty- 
eight  each,  and  Avery  in  thirty- two.  Three  of  the  four 
schools  giving  a  full  year  of  work  with  laboratory  work 
by  the  pupils  used  Rolfe  and  Gillet.  With  Steel's  Four- 
teen Weeks  in  one  quarter  of  the  schools,  it  is  evident  that 
the  "  short  informational  course,"  to  which  the  com- 
mittee of  ten  objected  so  strongly,  was  well  established 
by  this  time  (1880). 

14.  The  Nature  of  the  Course  in  1884.  —  The  second 
of  these  bulletins  (No.  7,  1884)  contains  letters  from 
thirty-two  secondary  schools,  seventeen  normal  schools, 
and  twenty-one  colleges.  These  letters  were  replies  to 
another  series  of  questions  sent  out  by  the  Bureau  of 
Education.  The  questions  asked,  among  other  things, 
for  expressions  of  opinion  on  the  following  points: 
i.  Whether  it  was  desirable  to  introduce  physics  (natural 
philosophy)  into  the  primary  and  grammar  schools,  and 
if  so,  to  what  extent.  2.  How  much  time  should  be 
given  to  it  in  high  school,  and  in  which  year  should  it 
come?  3.  Whether  physics  should  be  required  for  en- 
trance to  college  or  not.  4.  Whether  it  is  possible  to 
arrange  a  course  that  shall  satisfy  both  the  college  re- 


44  THE  TEACHING  OF  PHYSICS 

quirement  and  the  needs  of  the  schools.  5.  Whether  col- 
lege entrance  physics  should  differ  from  that  for  those  not 
going  to  college.  6.  What  should  be  the  prevailing  charac- 
ter of  the  high  school  course,  —  inductive  or  deductive, 
for  information  or  for  discipline,  whether  laboratory  work 
should  be  included  or  not,  and  how  much  mathematics 
should  be  assumed.  7.  What  are  the  main  reasons  for 
studying  physics  in  secondary  schools? 

The  summaries  of  the  replies  received  from  American 
schools,  to  which  is  added  a  summary  of  the  contemporary 
practice  and  opinion  in  England,  France,  and  Germany, 
is  worthy  of  careful  study.  While  there  is  large  diver- 
gence of  opinion  on  many  points,  there  is  very  general 
agreement  that  some  sort  of  science  should  be  taught  in 
grammar  schools;  and  that  this  science  should  be  in- 
troduced, not  for  the  sake  of  information,  but  for  the 
"  mental  training  and  discipline  which  the  pupils  acquire 
through  studying  the  methods  whereby  the  conclusions 
of  physical  science  have  been  established." 1  These 
elementary  courses  should  also  be  "  taught  in  each  kind 
of  school  for  the  benefit  of  those  who  will  go  no  farther  " 
(p.  1 1 6).  Suggestions  as  to  the  nature  of  this  elementary 
work  are  given  on  pages  126-128. 

As  to  the  time  to  be  devoted  to  physics  in  high  school, 
the  average  of  the  replies  gives  about  200  hours  as  de- 

1  Quoted  on  p.  115  from  British  Association  Reports  for  1871. 


PRESCRIBED  PHYSICS  45 

sirable.  The  year  in  which  it  should  be  given  is  "  pretty 
generally  stated  to  be  the  third  year  of  the  course,  ap- 
parently because  geometry  is  not  usually  given  before 
that  year.  The  suggestions  in  some  of  the  replies  that 
part  of  the  subject  be  taken  in  the  first  year,  and  the  re- 
mainder in  the  third  or  fourth,  deserves  careful  consid- 
eration. The  fundamental  ideas  and  ways  of  looking  at 
the  underlying  principles  of  the  subject  are  so  new  to  the 
student,  and  need  so  much  time  to  grow  into  shape  and 
to  have  any  real  meaning,  that  there  is  much  to  be  said 
in  favor  of  spreading  the  subject  over  a  considerable 
time"  (p.  129). 

As  to  the  desirability  of  requiring  physics  for  entrance 
to  college,  the  replies  are  summarized  as  follows  (p.  135) : 
"  The  study  of  physics  is  fitted  to  give  results  in  mental 
training  that  are  of  very  high  value  and  that  cannot  be 
given  so  well  by  other  studies;  it  is  to  be  considered  an 
essential  subject  in  the  secondary  schools;  in  these  it 
will  usually  be  better  taught  if  the  college  has  even  the 
slight  supervision  over  the  teaching  that  a  requirement 
for  admission  would  give,  and  so  this  requirement  would 
react  to  the  benefit  of  th,e  communities  where  these  schools 
are  situated.  .  .  .  No  more  powerful  influence  could 
be  exerted  to  improve  the  quality  of  the  teaching  than 
to  make  this  requirement  now  under  consideration,  and 
to  enforce  it  as  rigidly  as  any  other  requirement." 


46  THE  TEACHING  OF  PHYSICS 

It  is  interesting  to  note  in  passing  that  the  replies 
advocated  that  "  even  the  slight  supervision  over  the 
teaching  that  this  requirement  would  give  "  should  be 
"  enforced  as  rigidly  as  any  other  requirement."  Also, 
at  the  time  of  the  issue  of  this  bulletin  sixteen  of  the 
leading  colleges  already  had  this  requirement ;  and  others 
followed  suit  shortly  after,  until,  by  the  end  of  the  cen- 
tury, most  of  the  colleges  required  physics  for  entrance. 
Since  1900,  however,  the  colleges  have  been  gradually 
dropping  the  requirement  of  physics  for  entrance,  largely 
because  they  found  that  it  could  not  be  enforced.  The 
schools  did  not  require  it  for  graduation,  and  too  many 
students  without  it  applied  to  colleges  for  admission. 

Most  of  those  who  replied  to  the  questionnaire  agreed 
that  a  course  could  be  planned  that  would  satisfy  the 
requirements  both  of  college  entrance  and  of  the  schools. 
What  should  be  the  common  ground  of  such  a  course  was 
left  undecided,  and  the  suggestion  was  made  that  a  com- 
mittee of  college  and  high  school  men  be  appointed  by 
joint  action  of  the  National  Educational  Association  and 
the  American  Association  for  the  Advancement  of  Science 
to  settle  this  question  (p.  136). 

15.  Opinions  on  the  Method  of  Teaching  Physics  in 
1884.  —  As  to  methods  of  teaching  physics,  "  the  weight 
of  opinion  is  decidedly  that  at  first  the  teaching  should 
be  inductive"  (p.  117).  The  difficulties  in  the  way  of 


PRESCRIBED  PHYSICS  47 

securing  inductive  teaching  are  great,  because  "  the 
teacher  has  probably  known  little  or  nothing  of  it  in  his 
own  education,  and  does  not  know  how  to  begin.  If 
he  has  also  to  teach  mathematics,  he  is  especially  familiar 
with  deductive  methods  and  their  value  in  training. 
Again,  the  progress  of  the  student  following  the  induc- 
tive method  is  so  slow,  if  measured  by  the  usual  exami- 
nation tests,  as  to  discourage  a  faint  heart.  .  .  .  The 
common  advocacy  of  scientific  studies  for  the  value  of 
their  information  makes  it  more  difficult  to  follow  a 
method  in  which  information  is  a  subordinate  end. 
When  pushed  to  the  extreme,  the  method  breaks  down 
utterly ;  for  quantitative  experiments  are  mostly  beyond 
the  reach  of  high  school  boys,  yet  very  few  principles  or 
laws  can  be  established  without  them"  (p.  117). 

The  inductive  method  as  applied  to  teaching  is  thus 
described  (p.  118) :  "Following  the  scientific  method, 
we  first  observe  the  phenomena  sharply,  and  then  seek 
for  a  cause  or  for  the  law  according  to  which  the  forces 
act.  A  dozen  guesses  may  be  made  quickly,  perhaps  to 
be  found  insufficient.  But  if  the  guess  is  a  definite  one, 
definite  conclusions  (deductions)  can  be  drawn  from  it 
which  will  lead  to  new  observations  or  experiments. 
Perhaps  our  supposed  law  is  immediately  disproved; 
then  we  make  a  new  guess,  and  so  continue  until  one  ex- 
planation remains  which  is  consistent  with  all  our  knowl- 


48  THE  TEACHING  OF  PHYSICS 

edge  and  stands  all  the  tests  we  are  able  to  apply ;  and 
now  is  the  time  for  us  to  consult  the  published  record  of 
other  men's  experiments,  and  in  this  way  learn  those 
facts  that  are  otherwise  unattainable  by  us.  If  to  reason 
accurately  on  physical  facts  be  of  any  value  to  the  stu- 
dent, is  not  a  conclusive  disproof  of  an  hypothesis  (pro- 
vided he  originated  it)  more  valuable  than  the  incomplete 
proof  with  which  he  must  usually  remain  contented  when 
he  learns  the  accepted  hypothesis?  " 

Two  reasons  are  given  for  the  importance  of  using 
this  inductive  method  of  teaching,  namely  (p.  119) : 
i.  "  Because,  consciously  or  not,  we  must  use  inductive 
methods  all  our  lives  in  ways  where  we  cannot  avail 
ourselves  of  the  principle  of  the  division  of  labor,  de- 
pending on  others.  The  professional  opinions  of  the 
physician  and  lawyer,  all  our  judgments  of  men,  and 
our  opinions  on  common  matters  of  life  must  be  largely 
the  result  of  inductive  reasoning;  "  and  2.  "  Because  in 
the  opinion  of  many  teachers,  more  physics  can  be 
taught  so  as  to  be  remembered  in  this  way  than  in  any 
other." 

The  bulletin  then  shows  that,  notwithstanding  the 
obstacles  in  the  way  of  introducing  the  inductive  method, 
"  nearly  all  the  writers  of  the  replies  advise  it,  and  one 
cannot  believe  that  they  are  advising  so  unanimously 
an  impracticable  scheme.  Foreign  writers,  too,  are 


PRESCRIBED   PHYSICS  49 

very  unanimous  in  urging  it.  ...  The  Socratic  method, 
which  is  advocated  by  so  many  teachers  of  experience, 
is  really  the  inductive  method  put  in  a  form  suitable 
for  teaching.  The  use  of  textbooks  of  the  ordinary 
kind,  however  accurate  and  clear,  is  inconsistent  with, 
perhaps  almost  fatal  to,  the  scientific  method  in  schools  " 
(pp.  119-120). 

The  discussion  of  methods  of  teaching  is  summed  up 
again  on  page  130  in  these  words:  "The  majority  of 
the  replies  and  the  emphatic  English  opinions  already 
quoted  advise  that  the  teaching  should  be  inductive 
rather  than  deductive  (the  statement  of  principles  and 
laws  and  of  formal  definitions  coming  after  the  experi- 
ments rather  than  before  them  and  being  elicited  so 
far  as  practicable  from  the  student)  and  primarily  for 
discipline,  since  more  information  can  be  retained  and 
made  useful  if  the  mind  be  disciplined  than  if  the  mere 
information  be  the  end  of  the  study." 

"  Laboratory  work  is  favored  by  the  great  majority, 
though  sometimes  by  this  expression  is  evidently  meant 
merely  demonstration  by  the  teacher,  and  sometimes 
the  meaning  is  doubtful.  Unfortunately,  few  teachers 
can  speak  of  the  results  of  this  kind  of  teaching,  it  has 
been  tried  so  little,  except  in  the  normal  schools " 
(p.  130). 

"  With  regard  to  the  amount  of  mathematical  knowl- 


50  THE  TEACHING  OF  PHYSICS 

edge  to  be  assumed  there  is  the  greatest  diversity  of 
opinion.  The  general  view  may  be  said  to  be  that  the 
student  should  have  a  ready  command  of  arithmetic, 
of  algebra  through  equations  of  the  second  degree,  and 
of  elementary  geometry.  Of  these  the  first  is  least 
likely  to  be  secured,  for  the  drill  in  higher  arithmetic 
appears  to  be  at  the  expense  of  that  training  which  is 
the  most  useful  for  its  applications  in  physics,  viz.  that 
which  enables  the  pupil  to  solve  easy  problems  readily 
and  often  mentally.  Certainly  college  students  show 
the  lack  of  this  kind  of  training  to  an  unfortunate  de- 
gree "  (p.  131). 

As  to  the  importance  of  the  work  in  the  secondary 
school,  the  bulletin  says,  on  page  132  :  "In  considering 
how  the  study  of  physics  is  to  be  made  most  useful  to 
the  community,  both  directly  and  indirectly,  it  is  diffi- 
cult to  overestimate  the  importance  of  correct  views 
of  the  opportunities  of  the  secondary  schools.  Com- 
missioner Eaton's  tables  show  more  than  a  quarter  of 
a  million  students  in  them  and  only  an  eighth  as  many 
in  the  colleges.  These  students  are  young  enough  to 
retain  the  child's  love  of  nature  and  of  objective  teach- 
ing ;  yet  experience  shows  that  they  are  mature  enough 
to  profit  by  a  thorough  study  of  this  subject,  which  is 
one  of  the  very  best  for  inductive  training,  and  even 
those  who  are  to  have  further  opportunity  in  college 


PRESCRIBED  PHYSICS  51 

will  derive  benefit  from  having  their  intellectual  eyes 
opened  to  the  world  about  them.  .  .  .  On  the  other 
hand,  the  lower  schools  and  the  country  schools  draw 
their  teachers  largely  from  the  high  schools  and  the 
academies.  So  at  no  point  in  the  whole  system  is  the 
importance  of  good,  clear,  accurate,  inspiring  training  in 
physics  more  important  than  in  these  secondary  schools/' 
1 6.  The  First  Syllabus.  —  Finally  the  bulletin  closes 
with  a  list  of  fundamental  experiments  in  physics, 
"  which  may  be  shown  by  the  teacher,  or  some  of  them 
may  be  performed  by  the  student  in  the  laboratory. 
Besides  the  topics  involved  in  this  list  there  are  some 
others  of,  perhaps,  equal  importance  not  so  easily  illus- 
trated by  standard  experiments,  and  every  teacher  will 
/~^ 

perform  many  additional  experiments ;  but  this  list  is 
drawn  up  in  the  hope  that  the  few  experiments  it  con- 
tains may  everywhere  be  recognized  as  fundamental " 
(p.  146). 

This  list  is  here  given  in  full,  since  it  indicates  so 
clearly  what  was  considered  fundamental  to  a  course  in 
physics  in  1884.  A  f  means  fitted  for  laboratory  work ; 
a  §  involves  measurement;  an  *,  more  advanced. 

f§  Compare  and  measure  lengths,  tPr°Perties  of  permanent  and 

volumes,  and  masses.  temporary  magnets. 

t§  Composition  of  forces.  f  Magnetic  curves. 

Inertia.  f  Simple  galvanic  cell. 


THE  TEACHING  OF  PHYSICS 


f§  Parallel  forces. 
f  Center  of  gravity. 
f§  Lever,  inclined  plane,  &c. 
t§  Pendulum. 

*  Centrifugal  action. 

f§  Archimedes'  principle. 
f§  Density  and   specific  grav- 
ity. 

Capillarity. 
f§  Simple  barometer. 
§*  Boyle's  law. 

Air  pump  experiments. 
Pumps  and  siphon. 
f§  Expansion    of    liquids    and 

gases, 
f  Bending  of  compound 

bar. 

t§  Verify  fixed  points  of  ther- 
mometer. 

f    Conduction  of  heat. 
f§  Temperature  of  mixtures  of 

water. 

§*  Specific  heat  of  a  solid, 
f*  Latent  heat  of  ice,   steam, 

vapors. 
Heat  from  friction. 

*  Useful    forms    of    galvanic 

cells. 


f  Effects  of  current  on  mag- 
netic needle. 
f  Electro-magnets. 
§*  Influence  of  resistance  of  con- 
ductors, 
f  Chemical  effects  of  current. 

*  Heating  effects  of  current. 

*  Induction. 

Telegraph  and  telephone, 
f  Frictional    electricity ;    two 

states. 
Electrical  machine ;  Leyden 

jar. 
Vibration  and  production  of 

waves. 

f§  Resonance, 
f  Interference  of  sound  (fork 

and  jar). 
§  Monochord. 
f§  Photometer. 

Reflection ;  plane  and  curved 

mirror. 

f  Refraction  of  light. 
Dispersion  and  spectrum. 
Total  reflection. 
f§  Lenses;  construction  of 

image. 
Combination  of  colors. 


It  will  be  noted  that  no  mention  is  made  of  the  prin- 
ciple of  the  conservation  of  energy,  nor  are  any  units 
mentioned.  Even  work  does  not  appear,  nor  are  mole- 


PRESCRIBED  PHYSICS  53 

cules  and  atoms  and  the  kinetic  theory  of  matter  in 
evidence.  There  is  nothing  about  acceleration  nor 
about  falling  bodies  nor  about  Newton's  laws  of  motion. 
Yet  these  forty-seven  topics  were  considered  enough  to 
make  up  the  essentials  of  a  one-year  course  in  physics  in 
secondary  schools. 

So  much  space  has  been  devoted  to  this  bulletin  be- 
cause it  advocates  so  definitely  the  things  which  are 
now  so  badly  missed  in  the  high  school  courses  in  physics, 
—  inductive  teaching,  simple  experiments  in  familiar 
units,  and  training  in  the  scientific  method  of  thinking. 
These  ideas  found  frequent  expression  at  this  time 
(1884) ;  yet  in  spite  of  this,  they  were  not  followed  in 
the  subsequent  development  of  physics  teaching.  Now 
there  is  a  general  demand  for  a  reorganization  of  this 
teaching  in  conformity  with  the  ideas  that  were  so  promi- 
nent twenty-five  years  ago.1 

1  For  further  information  on  this  point,  the  reader  is  referred  to  Report 
of  the  Royal  Commission  on  Science  Instruction  and  the  Advancement  of 
Science,  9  vols.,  H.  M.  Stationery  Office,  1871-1875.  Reports  of  the 
British  Association  for  the  Advancement  of  Science,  1867,  pp.  xxxix-liv; 
1874,  p.  71 ;  1883,  p.  309.  In  the  London  Journal  of  Education,  articles 
by  Worthington,  October,  1882;  Wormell,  January,  1883;  Minchin, 
October,  November,  1883 ;  Jas.  Ward,  November,  1883 ;  in  Joseph  Payne's 
Collected  Lectures,  p.  187;  J.  M.  Wilson,  Essays  on  a  Liberal  Education; 
Report  of  Committee  of  the  American  Association  for  the  Advance- 
ment of  Science,  Proceedings,  1880,  pp.  55-63;  reprinted  in  Popular 
Science  Monthly,  Vol.  XXXIII,  p.  207. 


54  THE  TEACHING  OF  PHYSICS 

17.  The  Harvard  Descriptive  List.— The  next  impor- 
tant step  in  the  development  of  physics  teaching  was 
the  publication  of  the  well-known  Harvard  Descriptive 
List.  This  is  a  list  of  laboratory  experiments  only,  and 
was  issued  by  Harvard  College  in  1887  to  define  the 
laboratory  work  that  was  required  as  part  of  the  course 
acceptable  for  admission  credit  at  that  institution. 

This  list  contained  originally  forty-six  experiments, 
any  six  of  which  might  be  omitted.  "  The  choice  of 
experiments  required  careful  consideration.  .  .  .  The 
criterion  for  this  selection  was  that  of  practical  utility. 
An  attempt  was  made  to  bring  together  such  experi- 
ments as  would  have  the  most  frequent  and  important 
applications  in  ordinary  life,  in  the  conviction  that  these 
would  be,  on  the  whole,  quite  as  interesting  and  im- 
portant in  every  other  way  as  any  that  could  be  chosen 
under  a  different  principle  of  selection."  1 

From  the  preface  to  the  Descriptive  List  we  learn  that, 
"  The  objects  to  be  sought  in  the  course  of  experimental 
physics  which  this  pamphlet  describes  may  be  stated 
thus :  first,  to  train  the  young  student  by  means  of 
tangible  problems  requiring  him  to  observe  accurately, 
to  attend  strictly,  and  to  think  clearly;  second,  to  give 
practice  in  the  methods  by  which  physical  facts  and 
laws  are  discovered;  third,  to  give  practical  acquaint- 

1  Hall  &  Bergen,  Textbook  of  Physics,  p.  iv  (Holt,  1892). 


PRESCRIBED  PHYSICS  55 

ance  with  a  considerable  number  of  these  facts  and  laws, 
with  a  view  to  their  utility  in  the  thought  and  actions 
of  educated  men."  1 

"  With  very  few  exceptions  the  experiments  described 
will  require  the  student  to  make  measurements  of  some 
kind.  To  make  such  experiments  intelligible  and  prof- 
itable, they  must,  in  many  cases,  be  supplemented  by 
other  experiments  of  a  less  rigorous  character,  such  as 
are  described  in  the  textbooks  of  Avery,  Gage,  and 
various  other  authors,  and  many  of  which  are  better 
fitted  for  exhibition  on  the  lecture  table  than  for  per- 
formance by  each  student  of  the  class.  .  .  .  The  direc- 
tions given  in  this  pamphlet  are  in  some  cases  very 
minute.  They  are,  however,  intended  to  show  how  the 
experiments  may  be  done,  not  how  they  must  be  done. 
The  teacher  should  decide  for  himself  how  closely  these 
directions  are  to  be  followed,  and  should  feel  at  liberty 
to  substitute  for  the  experiments  described  other  ex- 
periments covering  equally  well  the  same  points.  .  .  . 
This  course  in  all  its  aspects  is  intended  to  occupy 
the  student  about  five  school  hours  a  week,  with  the 
usual  amount  of  study  out  of  school,  for  one  year."  2 

"  To  secure  the  objects  of  the  course  the  student 
during  the  laboratory  exercises  is  placed,  so  far  as  this 
is  practicable,  in  the  attitude  of  an  investigator  seeking 
1  Hall  &  Bergen,  I.e.,  p.  vii.  »  Ibid.,  p.  x. 


56  THE  TEACHING  OF  PHYSICS 

for  things  unf  ore  told.  But  this  attitude,  if  rigidly 
maintained,  would  be  likely  to  keep  him  for  an  absurdly 
long  time  upon  the  study  of  one  set  of  facts,  or  induce 
the  habit  of  loose  and  hasty  generalization.  He  should 
be  required  to  work  carefully,  but  not  with  a  higher 
standard  of  accuracy  than  the  apparatus  and  the  time 
at  his  disposal  will  warrant.  He  should  not  be  told 
what  he  is  expected  to  see,  but  he  must  usually  be  told 
in  what  direction  to  look.  He  should  be  required  to 
draw  inferences  from  his  experiments,  but  the  sources 
of  possible  or  certain  error  in  his  work  should  be  pointed 
out  in  order  that  he  may  be  saved  from  the  danger  of 
coming  to  think  that  all  so-called  physical  laws  are  in- 
ferred from  demonstrations  as  loose  as  his  own.  In 
fact,  the  main  value  of  the  student's  inferences,  in  them- 
selves, is  that  they  will  enable  him  to  understand,  and 
without  undue  stretch  of  faith  to  accept,  the  established 
conclusions  of  physicists,  and  these  conclusions  should, 
in  the  end,  always  be  made  known  to  him."1 

Because  of  the  great  influence  which  this  list  has 
exerted  on  physics  teaching,  that  portion  which  deals 
with  mechanics  will  be  reprinted  in  the  form  in  which  it 
appears  in  the  Hall  &  Bergen  Textbook  of  Physics. 

1.  Breaking  strength  of  a  wire. 

2.  Elasticity,  stretching. 

1  Hall  &  Bergen,  I.e.,  p.  xi. 


PRESCRIBED  PHYSICS  57 

3.  Elasticity,  bending. 

4.  Elasticity,  twisting. 

5.  Pressure  in  a  liquid. 

6.  Compressibility  of  air. 

7.  Density. 

8.  Specific  gravity  of  a  solid  that  will  sink  in  water. 

9.  Specific  gravity  of  a  solid  that  will  float  in  water. 

10.  Specific  gravity  of  a  liquid. 

11.  Specific  gravity  of  air ;  degree  of  exhaustion. 

12.  Composition  of  forces. 

13.  Coefficient  of  friction. 

14.  15.   Parallel  forces  in  one  plane. 

16.  Forces  in  one  plane,  but  not  parallel. 

17.  Center  of  gravity ;  influence  of  the  weight  of  a  lever. 

1 8.  Inertia:  comparison  of  masses. 

19.  Simple  pendulum. 

20.  Action  and  reaction. 

21.  The  inclined  plane ;   work. 

As  has  been  stated,  this  Descriptive  List  contains 
only  laboratory  experiments,  with  careful  directions  as 
to  how  the  experiments  may  be  performed.  The  teacher 
was  left  to  fill  up  the  rest  of  his  course  as  best  he  might. 
In  order  to  help  the  teacher  in  doing  this,  Hall  &  Bergen 
published  their  Textbook  of  Physics  in  1892. 

A  comparison  of  this  list  with  that  from  the  Bulletin 
No.  7,  as  given  above,  shows  how  great  an  advance  has 
been  made  in  the  definiteness  of  the  specification  of  the 
experiments.  For  example,  the  topic  "  Inertia "  in 
the  first  list  may  mean  any  number  of  things;  but  the 


58  THE  TEACHING  OF  PHYSICS 

topic  "  Inertia :  comparison  of  masses/'  accompanied 
by  full  directions  as  to  how  to  proceed  with  the  experi- 
ment, is  perfectly  definite  and  a  very  certain  guide  to 
the  teacher  who  is  preparing  boys  to  get  entrance  credit 
at  Harvard.  There  can  be  no  doubt  that  this  definite- 
ness,  both  in  title  and  in  detail  of  description  of  manip- 
ulation, of  the  Harvard  Descriptive  List  is  one  of  the 
chief  elements  of  its  power  and  usefulness.  At  the  time 
of  its  publication,  teachers  of  physics  were  scarce,  there 
were  few  laboratories  and  little  experience  to  guide  those 
who  wished  to  introduce  this  work,  so  this  sort  of 
guidance  was  essential  to  the  successful  establishment 
of  experimental  courses  in  physics. 

The  influence  of  the  Descriptive  List  on  the  develop- 
ment of  physics  teaching  in  America  has  been  tremen- 
dous. It  appeared  at  the  psychological  moment  when 
the  demand  for  object  teaching,  which  had  made  its  ap- 
pearance here  about  1848,  had  reached  its  full  force.  It 
exalted  this  demand  for  object  teaching  into  a  require- 
ment of  quantitative  laboratory  work.  It  showed  teachers 
and  school  boards  how  a  laboratory  method  of  teaching 
could  be  introduced  into  the  work  in  physics  with  the  use 
of  materials  at  hand  and  with  a  small  outlay  for  equip- 
ment. Its  insistence  on  careful,  neat  work,  and  its  firm 
stand  for  work  of  a  scientific  character  made  its  influence 
on  physics  teaching  a  most  salutary  one  for  many  years. 


PRESCRIBED  PHYSICS  59 

Some  idea  of  the  magnitude  and  the  importance  of 
the  change  that  has  come  about  under  the  influence  of 
this  list  may  be  had  by  noting  that  in  1880  there  were 
but  four  schools  in  the  country  giving  a  full  year's  work 
in  physics  with  laboratory  work  by  the  pupils.1  Is 
there  to-day  any  school  in  which  physics  is  taught  which 
has  not  its  "  physics  laboratory  "  and  its  modicum  of 
apparatus  for  laboratory  work  by  the  pupils  ?  And 
who  can  estimate  the  effect  of  this  growth  of  the  labora- 
tory method  in  physics  on  the  similar  growth  in  the 
other  sciences?  As  the  result  of  this  movement,  the 
American  public  high  schools  now  have  laboratories, 
while  the  schools  in  France  and  Germany  are  just  be- 
ginning to  secure  them. 

18.  The  Committee  of  Ten.  —  The  next  important 
official  contribution  to  the  development  of  physics 
teaching  is  the  report  of  the  Conference  of  Physics, 
Chemistry,  and  Astronomy  to  the  Committee  of  Ten.2 
This  report  recommends  (p.  119):  "That  physics  be 
pursued  the  last  year  of  the  high  school  course,  in  order 
that  the  pupils  should  have  as  much  mathematical  knowl- 
edge as  possible  to  enable  them  to  deal  satisfactorily 
with  the  subject;  "  that  physics  be  required  for  admission 
to  college;  that  it  be  taught  by  "  a  combination  of  labora- 
tory work,  textbook,  and  thoroughly  didactic  instruc- 

1  Ante,  p.  42.          2  Report  of  the  Committee  of  Ten,  pp.  117-127. 


60  THE  TEACHING  OF  PHYSICS 

tion;  "  that  the  laboratory  work  should  be  largely  quan- 
titative; and  that  the  aim  of  the  teaching  should  not  be 
"  to  make  a  so-called  rediscovery  of  the  laws  of  physics," 
but  that  the  pupils  should  "  determine  the  elasticity  of 
bending  wood  as  to  length,  breadth,  and  thickness,  and 
see  whether  the  results  agree  with  the  laws." 

A  list  of  "  experiments  that  by  common  consent  are 
used  by  several  authors  "  is  given  as  suggestive  to  those 
teachers  who  wish  to  "  know  the  kind  and  degree  of 
difficulty  of  experiments  suitable  for  preparation  for 
admission  to  college  in  physics."  This  list  contains 
fifty-one  experiments.  It  differs  from  the  Harvard 
Descriptive  List  in  only  two  important  points;  namely, 
it  adds,  "  Find  the  coordinates  of  a  given  curve  drawn 
on  coordinate  paper,  and  plot  a  curve  from  given  co- 
ordinates; "  and  "  Relation  of  the  acceleration  of  falling 
bodies  to  the  moving  force."  These  two  additions, 
together  with  the  ideas  that  physics  should  come  in 
the  fourth  year  in  order  to  insure  satisfactory  mathe- 
matical knowledge,  and  .that  the  experiments  were 
"  suitable  for  preparation  for  admission  to  college," 
indicate  the  gravitation  toward  the  university  physics 
and  toward  the  colleges  which  had  taken  place  in  the 
interval  between  1884  and  1893. 

19.  The  National  Physics  Course.  —  The  Report  of 
the  Committee  on  College  Entrance  Requirements  also 


PRESCRIBED   PHYSICS  6l 

contains  a  section  devoted  to  physics  (pp.  180-182). 
As  regards  this  section,  the  general  committee  says 
(p.  23) :  "  So  far  as  the  reports  in  our  possession  have 
enabled  us  to  do  so,  we  have  indicated  in  some  detail 
what  the  character  of  these  courses  in  science  should  be. 
Unfortunately,  this  has  been  impossible  in  the  cases  of 
physics  and  zoology,  and  we  recommend  that  the  Com- 
mittee on  Physics  appointed  by  the  Natural  Science 
Section  of  the  National  Educational  Association  be  again 
requested  to  supply  detailed  descriptions  of  suitable 
school  courses  in  these  sciences." 

The  general  committee  further  recommends  (p.  25) : 
that  the  physics  course  in  secondary  schools  occupy  not 
less  than  one  year  of  daily  exercises  (one  unit) ;  that  it 
include  a  large  amount  of  laboratory  work,  mainly 
quantitative ;  that  the  laboratory  work  occupy  approxi- 
mately one  half  the  time;  that  the  course  also  include 
instruction  by  textbook  and  lecture,  with  qualitative 
experiments  by  the  teacher,  all  "  to  the  end  that  the  pupil 
may  gain  not  merely  empirical  knowledge,  but,  so  far  as 
this  may  be  practicable,  a  comprehensive  and  connected 
view  of  the  most  important  facts  and  laws  of  elementary 
physics." 

When  we  recall  that  in  the  Harvard  Descriptive  List 
11  an  attempt  was  made  to  bring  together  such  experi- 
ments as  would  have  the  most  frequent  and  important 


62  THE  TEACHING  OF  PHYSICS 

applications  to  ordinary  life,"  the  way  in  which  the  point 
of  view  changed  between  1887  and  1899  is  at  once 
apparent.  It  is  no  longer  a  question  of  "  Practical 
acquaintance  with  these  facts  and  laws,  with  a  view  to 
their  utility  in  the  thought  and  action  of  educated  men:  " l 
but  of  a  "  comprehensive  and  connected  view  of  the  most 
important  facts  and  laws  of  elementary  physics." 

Besides  the  recommendations  by  the  general  committee, 
the  report  contains  (pp.  180-182)  an  "  Outline  of  Labora- 
tory Work  in  Physics  for  Secondary  Schools."  The 
origin  of  this  outline  is  explained  in  full  by  its  author, 
Professor  E.  H.  Hall,  who  was  chairman  of  the  physics 
committee,  in  his  book  on  the  Teaching  of  Physics  in 
Secondary  Schools  (pp.  3  2  7-33  5)  .2  We  there  read 
(p.  329) :  "  In  this  supplementary  part  of  the  report 
the  matter  relating  to  physics  is  little  more  than  the 
Table  of  Contents  of  the  Harvard  Descriptive  List  and 
two  paragraphs  taken,  almost  without  change,  from  the 
introduction  to  that  list." 

In  speaking  of  this  physics  section  of  this  report, 
which,  as  has  just  been  noted,  consists  of  a  list  of  labora- 
tory experiments  only,  Professor  Hall  says:3  "On  the 
subject  of  this  chapter  (Physics  in  Various  Kinds  of  Sec- 

1  Ante,  p.  54. 

2  Smith  &  Hall,  Teaching  of  Chemistry  and  Physics  in   Secondary 
Schools,  pp.  xiii-377  (New  York,  Longmans,  Green,  &  Co.,  1902). 

» Ibid.,  p.  327. 


PRESCRIBED  PHYSICS  63 

ondary  Schools)  we  have  something  approaching  the 
authority  of  official  utterance  in  the  various  publications 
of  the  National  Educational  Association  during  the  past 
ten  or  twelve  years."  Passing  over  the  question  as  to 
what  may  be  meant  by  the  "  authority  of  official  utter- 
ance "  in  matters  educational,  we  note,  as  did  the  general 
committee,1  that  the  aforementioned  "  authorities " 
gave  no  "  official  utterance  "  to  guide  the  teacher  in 
his  class-room  work.  Hence  the  most  important  func- 
tion of  selecting  subject  matter  other  than  that  of  the 
laboratory,  and  of  choosing  an  appropriate  method  of 
presentation,  was  left  to  the  textbook  writers  (not  to 
mention  the  publishers)  and  to  the  lesser  organizations  of 
teachers  less  able  to  give  vent  to  "  official  utterances." 
The  way  in  which  the^textbooks  have  used  this  freedom 
from  the  authority  that  works  from  above  downward  will 
be  considered  in  the  next  chapter. 

Immediately  after  the  adoption  of  the  Report  of  the 
Committee  on  College  Entrance  Requirements,  including, 
as  it  did,  the  Harvard  Descriptive  List,  now  backed  up 
by  the  "  authority  of  official  utterance,"  several  appa- 
ratus companies  put  on  the  market  complete  outfits 
capable  of  "  doing  "  all  the  experiments  in  this  list. 
The  companies  advertised  these  outfits  widely,  stating 
that  they  were  especially  designed  to  enable  the  pupils 
1  Ante,  p.  61. 


64  .THE  TEACHING  OF  PHYSICS 

to  perform  all  the  experiments  required  by  what  the 
companies  called  the  "  National  Physics  Course."  These 
outfits  were  sold  extensively  throughout  the  country, 
and  exerted  a  powerful  influence  toward  fixing  the  nature 
of  the  course  and  that  of  each  experiment,  and  toward 
encouraging  schools  to  introduce  laboratory  work  of  the 
kind  specified,  because  they  furnished  an  easy  means 
of  doing  so,  and  one  which  did  not  require  the  teacher 
to  be  too  much  of  a  specialist  in  physics. 

How  firmly  this  "  National  Physics  Course  "  became 
intrenched  was  shown  by  an  investigation  conducted  by 
a  committee  of  the  Central  Association  of  Science  and 
Mathematics  Teachers  in  1906.*  The  committee  sent 
out  a  questionnaire  containing  a  list  of  one  hundred 
and  one  experiments  used  in  secondary  schools.  Each 
teacher  was  asked  to  indicate  those  experiments  which 
he  regarded  as  essential  to  the  course,  and  also  those 
which  he  had  found  most  successful  with  the  students. 
Two  hundred  and  seventy-five  replies  were  received 
from  teachers  in  all  parts  of  the  country.  Forty-seven 
experiments  were  voted  essential  to  the  course  by  a 
majority  of  those  who  replied ;  and  twenty-nine  of  these 
were  declared  to  be  essential  by  two  thirds  of  those 
who  replied.  Of  the  forty-seven  experiments  chosen  by 

1  A  New  Movement  among  Physics  Teachers,  Circular  II,  School 
Review,  Vol.  XIV,  p.  429,  June,  1906. 


PRESCRIBED  PHYSICS  65 

the  majority,  thirty-six  are  contained  in  the  Harvard 
list  as  it  appeared  in  the  Report  of  the  Committee  on 
College  Entrance  Requirements;  and  of  the  twenty- 
nine  chosen  by  two  thirds  of  the  teachers  voting,  twenty- 
six  are  contained  in  that  list. 

There  can  be  no  doubt,  as  has  been  shown  abundantly 
above,  that  the  Harvard  Descriptive  List  was,  at  the  time 
of  its  publication  (1887)  and  for  a  number  of  years  after 
that,  a  very  useful  document.  It  helped  to  create  a 
demand  for  laboratory  work,  which  has  resulted  in  the 
establishment  of  high  school  laboratories.  It  supplied 
teachers  and  schools  with  valuable  suggestions  as  to 
ways  and  means  of  equipping  laboratories  at  a  cost  that 
was  not  prohibitive.  Its  insistence  upon  quantitative 
work  aroused  teachers  to  an  appreciation  of  the  need  and 
the  value  of  making  measurements.  When,  however, 
it  became  clothed  with  the  "  authority  of  official  utter- 
ance," and  was  baptized  "  National  Physics  Course  " 
by  the  apparatus  dealers,  its  vitality  was  gone.  It  has 
now  become  an  institutionalized  form,  which,  like  all 
such  forms,  first  blocks  the  way  of  progress,  and  then 
fades  away. 

20.  The  New  York  State  Syllabus.  —  The  failure  of 
the  Committee  on  College  Entrance  Requirements  to 
outline  the  subject  matter  for  the  class  work  in  physics 
soon  led  to  trouble  in  those  places  where  the  work  of  the 


66  THE  TEACHING  OF  PHYSICS 

secondary  school  was  tested  by  examinations  set  by  an 
authority  outside  the  school.  It  is  clear  that  in  places 
where  such  examinations  are  considered  desirable,  there 
must  be  some  sort  of  an  agreement  between  the  examin- 
ing bodies  and  the  teachers  as  to  the  nature  of  the  work 
and  the  nature  of  the  examination.  It  was,  doubtless, 
to  meet  this  need  that  the  New  York  State  Department 
of  Education  issued  its  Topical  Syllabus  in  Physics  in 
1905. 

This  syllabus  contains  260  topics,  and  is  a  model  of 
what  is  usually  called  logical  order.  It  was  revised  in 
1910  by  the  addition  of  a  few  more  topics.  When  we 
recall  that  a  unit  in  physics  is  denned  as  120  hours  of 
class  work,  we  see  that  this  syllabus  allows  the  teacher 
less  than  half  an  hour  to  teach  each  topic,  including 
demonstrations,  laboratory  exercises,  quizzes,  etc. 

In  like  manner,  the  College  Entrance  Examination 
Board  has  issued  a  new  syllabus  as  a  basis  for  conducting 
its  examinations.1  This  syllabus  contains  170  topics, 
and  is  an  abridgment  of-  the  New  York  State  Syllabus. 
It  is  an  interesting  document  because  it  was  compiled  by 
a  committee  consisting  of  six  secondary  school  teachers  v/ 

1  Definition  of  the  Requirement  in  Physics,  School  Science  and  Mathe- 
matics, Vol.  IX,  p.  572,  June,  1909;  Vol.  X,  p.  34,  January,  1910; 
Educational  Review,  Vol.  37,  p.  532,  May,  1909;  Vol.  38,  p.  150,  Septem- 
ber, 1909. 


PRESCRIBED  PHYSICS  67 

of  physics,  without  any  help  from  the  colleges.  This 
syllabus  is  thus  a  fairly  accurate  presentation  of  the 
consensus  of  present  opinion  among  secondary  school 
men  as  to  what  constitutes  a  reasonable  ground  for 
college  entrance  examinations  in  physics. 

21.  The  North-Central  Syllabus.  —  One  other  topical 
syllabus  of  importance  has  recently  been  issued  (1907) 
by  the  North  Central  Association  of  Colleges  and  Sec- 
ondary Schools.1  This  syllabus  was  not  designed  to 
define  the  limits  of  examinations,  for  practically  no 
examinations  are  given  by  authorities  outside  the  school 
in  the  North  Central  States.  It  was  compiled  by  the 
National  Commission  on  the  Teaching  of  Physics2  by 
a  method  of  exclusion,  and  contains  only  those  topics 
to  which  no  objection  was  made  by  any  one  of  the  fifty- 
five  members  of  that  commission.  It  contains  eighty-one 
topics,  and  represents,  because  of  its  method  of  compila- 
tion, the  consensus  of  opinion  concerning  the  essentials 
of  a  high  school  course  in  physics  at  the  present  time. 
Because  of  the  small  number  of  topics,  it  allows  large 
possibilities  for  the  variation  of  courses  to  suit  local 
needs,  yet  retains  sufficient  uniformity  to  furnish  a 
basis  for  college  entrance  examinations  and  subsequent 

1  Proceedings  of  the  North  Central  Association,  1910,  p.  37 ;  School 
Science  and  Mathematics,  Vol.  VIII,  p.  522,  June,  1908.       / 

2  School  Review,  Vol.  XIV,  p.  658,  November,  1906.     * 


68  THE  TEACHING  OF  PHYSICS 

work  in  college  for  those  who  go  on  to  a  further  study  of 
physics. 

This  syllabus  is  significant,  not  so  much  because  of 
what  it  contains,  as  because  of  what  it  omits.  The  devel- 
opment of  physics  in  the  universities  had  carried  into  the 
secondary  school  work  a  large  amount  of  abstract  work 
with  absolute  units,  accelerated  motion,  kinetic  theory 
of  gases,  and  the  like.  These  are  entirely  omitted  from 
this  syllabus.  The  topics  are  stated  in  rather  general 
terms,  yet  terms  which  have  a  specific  meaning  to 
physics  teachers  now.  Its  treatment  of  mechanics  is 
as  follows :  — 

1.  Weight,  center  of  gravity. 

2.  Density. 

3.  Parallelogram  of  forces. 

4.  Atmospheric  pressure,  barometer. 

5.  Boyle's  law. 

6.  Pressure  due  to  gravity  in  liquids  with  a  free  surface ;  vary- 
ing depth,  density,  and  shape  of  vessel. 

7.  Buoyancy,  Archimedes'  principle. 

8.  Pascal's  law;  hydraulic  press. 

9.  Work  as  force  times  distance,  and  its  measurement  in  foot 
pounds  and  gram  centimeters. 

10.  Energy  measured  by  work. 

11.  Law  of  machines;  work  obtained  not  greater  than  work 
put  in ;  efficiency. 

12.  Inclined  plane. 

13.  Pulleys;  wheel  and  axle. 

14.  Measurement  of  moments  by  force  X  arm ;  levers. 


PRESCRIBED   PHYSICS  69 

In  regard  to  quantitative  work,  the  introduction  to 
this  syllabus  says :  "  At  least  twenty  of  the  laboratory 
experiments  should  involve  numerical  work  and  the 
determination  of  such  quantitative  relations  as  may  be 
expressed  in  whole  numbers.  Such  quantitative  work 
should  aim  to  foster  the  habit  of  thinking  quantitatively, 
but  should  not  attempt  to  verify  laws  with  minute 
accuracy  nor  to  determine  known  physical  constants 
with  elaborate  apparatus.  .  .  .  The  class  work  should 
aim  to  build  up  in  the  student's  mind  clear  concepts  of 
physical  terms  and  quantities,  and  an  intuitive  apprecia- 
tion of  the  general  principles  which  make  up  the  syllabus. 
He  must  be  trained  in  the  use  of  those  principles  in  the 
solution  of  simple,  practical,  concrete  numerical  prob- 
lems."1 

22.  Uses  and  Abuses  of  Syllabi.  —  Whenever  a 
syllabus  is  regarded  by  a  teacher  as  merely  suggestive, 
but  not  binding,  its  effect  may  be  very  good.  Unfortu- 
nately, recent  practice  has  shown  that  this  is  not  likely 
to  be  the  case  when  the  syllabus  is  enforced  by  an  au- 
thority outside  the  school.  Under  this  system,  teachers 
know  well  that  it  is  necessary  that  their  pupils  make 
good  showings  at  examination  time.  Hence  the  teacher 
feels  compelled  to  "  cover  "  every  topic  in  the  syllabus 
at  any  cost.  Under  this  system  educational  experimen- 
1  Proceedings  of  the  North  Central  Association,  1910,  p.  38. 


70  THE  TEACHING  OF  PHYSICS 

tation  is  at  a  standstill,  and  the  adaptation  of  the  course 
to  local  needs  is  well  nigh  impossible. 

The  workings  of  this  system  of  examinations  by  au- 
thorities outside  the  school  is  thus  described  by  the  Com- 
mittee on  Curricula  of  Secondary  Schools  of  the  British 
Association  for  the  Advancement  of  Science  in  their  re- 
port to  that  association  at  its  Dublin  meeting  in  1908 
(p.  534):  "  We  are  struck  with  the  unanimity  shown  by 
our  correspondents  concerning  the  influence  of  external 
examinations  on  the  teaching  of  science.  This  influence 
is  found  to  be  harmful.  The  harm  is  produced  partly 
by  having  to  work  along  the  lines  of  too  rigid  a  syllabus, 
but  chiefly  by  the  fact  that  science  is  intended  to  teach 
principles,  while  the  examination  asks  for  details.  A 
boy  may  have  derived  the  full  benefit  from  a  course  of 
science  lessons  without  remembering  the  experiments 
therein;  for  the  examination,  however,  he  has  not  to  re- 
peat these  experiments;  he  has  to  memorize  them,  and 
to  study  how  to  reproduce  what  he  remembers  in  the 
approved  examination  style.  Anything  farther  from 
true  scientific  method  could  not  possibly  be  conceived. 

"  Working  on  the  lines  of  a  prescribed  syllabus  limits 
the  teacher's  initiative  and  discourages  research  methods. 
The  syllabus  in  nearly  all  cases  prescribes  too  much  for 
the  majority  of  schools;  and,  therefore,  too  much  is  at- 
tempted in  the  schools.  This  prevents  sufficient  atten- 


PRESCRIBED  PHYSICS  71 

tion  to  the  scientific  method  of  inquiry.  All  the  school 
work  in  science  should  be  imbued  with  the  aim  of  culti- 
vating an  appreciation  of  and  familiarity  with  scientific 
method.  Examinations  will  continue  to  impede  this  aim 
in  so  far  as  the  school  work  is  forced  to  conform  to  the 
examinations  rather  than  vice  versa" 

The  results  of  enforcing  syllabi  by  external  examina- 
tions are  the  same  in  America  as  in  England.  While 
this  practice  may  yield  excellent  results  in  the  human- 
ities, it  is  perfectly  clear,  for  the  reasons  just  given,  that 
it  has  been  fatal  to  the  development  of  vital  teaching  of 
science. 

Prior  to  the  publication  of  its  syllabus,  the  College 
Entrance  Examination  Board  exercised  a  similar  unfor- 
tunate influence  in  schools  where  one  or  more  pupils  were 
being  prepared  for  these  examinations.  The  questions  of 
the  past  examinations  were  th^n  the  laws  of  the  Medes 
and  the  Persians  for  the  teacher,  and  he  was  very  prone 
to  cram  his  pupils  on  these  stale  questions  until  those 
who  were  going  to  the  examination  could  recite  the  whole 
list  by  heart.  The  new  syllabus  is  still  too  new  to  trace 
its  effects ;  but  since  the  number  of  topics  in  it  is  only 
170,  there  is  some  chance  of  teaching  it  all  with  some 
degree  of  efficiency,  and  at  the  same  time  of  adapting 
the  course  to  local  needs. 

In  the  West,  college  demands  are  enforced  entirely 


72  THE  TEACHING  OF  PHYSICS 

by  the  inspection  and  accrediting  system.  This  system 
is  no  less  effective  a  means  of  keeping  the  schools  in  line 
than  is  the  examination  system.  Since  the  Western 
colleges  have,  until  recently,  dreaded  being  charged 
with  "  lowering  standards "  (standards  being  unde- 
fined) ,  they  have  maintained  the  same  sort  of  work  that 
has  been  demanded  by  the  College  Entrance  Examina- 
tion Board.  This  condition  is  now  rapidly  passing  away. 
The  colleges  in  the  North  Central  Association  agree  to 
admit  without  examination  pupils  from  schools  that  live 
up  to  the  rules  and  definitions  of  that  body.  Since  the 
definition  of  the  physics  unit  that  is  now  in  use  by  that 
association  has  but  eighty-one  topics  in  its  syllabus,  the 
teachers  of  the  middle  West  are  free  to  make  experiments 
in  teaching  within  very  wide  limits.  The  results  of 
this  freedom  are  beginning  to  appear  in  some  excellent 
experiments  like  those  in  the  Englewood  High  School, 
Chicago,1  those  in  the  high  school  at  Menomonie,  Wis., 
and  elsewhere. 

1  Tower,  School  Science  and  Mathematics,  Vol.  XI,  p.  i,  January,  1911. 


CHAPTER  IV 

TEXTBOOKS  OLD  AND  NEW 

23.  The  Problem  not  yet  Solved.  —  In  the  preceding 
chapter  attention  has  been  called  to  the  demand  that 
physics  be  taught  inductively,  in  order  that  the  pupil 
might  learn  to  think  scientifically.  In  order  to  secure 
this  sort  of  training,  the  teachers  of  the  past  generation 
fought  for  laboratories  and  equipment ;  and  "  when  the 
battle  was  on,  men  lost  their  heads  —  men  must  lose 
their  heads  in  order  to  fight.  We  thought  that  if  we 
could  get  laboratories,  the  problems  of  education  would 
be  solved."  1 

"  Now  science  is  recognized;  we  have  laboratories 
everywhere,  and  laboratory  training  is  regarded  as  indis- 
pensable. It  is  therefore  fitting  to  ask:  What  are  we 
doing  with  our  facilities?  What  results  are  we  obtain- 
ing? Do  the  results  obtained  justify  the  equipment 
and  time  devoted  to  scientific  study  ?  I  am  not  qualified 
to  answer  these  questions  for  the  schools ;  but,  speaking 
for  the  colleges,  I  may  say  that  in  my  opinion  the  results 

1  Remsen,  School  Science  and  Mathematics,  Vol.  DC,  p.  281,  March,  1909. 

73 


74  THE  TEACHING  OF  PHYSICS 

are  frequently  quite  unsatisfactory.  The  reason  is 
that  we  have  not  yet  learned  how  to  deal  with  the 
subject.  It  is  not  hard  to  teach  chemists  chemistry, 
but  it  is  very  hard  to  teach  beginners  something  that  is 
worth  while  about  chemistry  in  one  year." 1 

The  reason  why  the  mere  acquisition  of  laboratories 
and  the  introduction  of  laboratory  work  by  the  pupils 
have  not  solved  the  problem  of  training  the  pupils  in 
scientific  thinking  is  thus  given  by  Dewey  :2  "  A  student 
may  acquire  laboratory  methods  as  so  much  isolated 
and  final  stuff,  just  as  he  may  so  acquire  material  from 
a  textbook.  One's  mental  attitude  is  not  necessarily 
changed  just  because  he  engages  in  certain  physical  ma- 
nipulations and  handles  certain  tools  and  materials. 
Many  a  student  has  acquired  dexterity  and  skill  in  labora- 
tory methods  without  its  ever  occurring  to  him  that 
they  have  anything  to  do  with  constructing  beliefs  that 
are  alone  worthy  of  the  title  of  knowledge.  To  do  cer- 
tain things,  to  learn  certain  modes  of  procedure,  are  to 
him  just  a  part  of  the  subject  matter  to  be  acquired ; 
they  belong,  say,  to  chemistry,  just  as  do  the  symbols 
H2S04  or  the  atomic  theory.  They  are  part  of  the 
arcana  in  process  of  revelation  to  him.  In  order  to 
proceed  in  the  mystery  one  has,  of  course,  to  master 

1  Remsen,  I.e.,  p.  282. 

2  Dewey,  Science,  Vol.  XXX,  p.  125,  Jan.  28, 1910. 


TEXTBOOKS  OLD   AND   NEW  75 

its  ritual.  And  how  easily  the  laboratory  becomes 
liturgical !  In  short,  it  is  a  problem  to  conduct  matters 
so  that  the  technical  methods  employed  in  a  subject 
shall  become  conscious  instrumentalities  of  realizing 
the  meaning  of  knowledge  —  what  is  required  in  the 
way  of  thinking  and  of  search  for  evidence  before  any- 
thing passes  from  the  realm  of  opinion,  guesswork,  and 
dogma  into  that  of  knowledge.  Yet  unless  this  per- 
ception accrues,  we  can  hardly  claim  that  an  individual 
has  been  instructed  in  science.  This  problem  of  turning 
laboratory  technique  to  intellectual  account  is  even  more 
pressing  than  that  of  utilization  of  information  derived 
from  books.  Almost  every  teacher  has  had  drummed 
into  him  the  inadequacy  of  mere  book  instruction,  but 
the  conscience  of  most  is  quite  at  peace  if  only  pupils 
are  put  through  some  laboratory  exercises.  Is  not  this 
the  path  of  experiment  and  induction  by  which  science 
develops?  Communication  of  science  as  subject  matter 
has  so  far  outrun  in  education  the  construction  of  a 
scientific  habit  of  mind  that  to  some  extent  the  natural 
common  sense  of  mankind  has  been  interfered  with  to 
its  detriment." 

In  like  vein,  W.  S.  Franklin  says,  "  My  experience  is, 
most  emphatically,  that  a  student  may  measure  a  thing 
and  know  nothing  at  all  about  it ;  and  I  believe  that  the 
present  high  school  courses  in  elementary  physics,  in 


76  THE  TEACHING  OF  PHYSICS 

which    quantitative    laboratory    work    is    so    strongly 
emphasized,  are  altogether  bad."  1 

24.  The  Method  of  the  Texts;  Definitions.  —  In 
order  to  test  the  statements  that  the  mere  acquisition  of 
laboratories  has  not  solved  the  problems  of  education, 
and  that  the  value  of  the  training  derived  from  a  study 
of  science  depends  entirely  on  how  the  work,  both  in  the 
classroom  and  in  the  laboratory,  is  done,  we  will  try  to 
find  out  how  this  work  has  been  and  is  done.  Unfortu- 
nately, it  is  now  impossible  to  visit  the  classes  of  bygone 
years ;  so  we  shall  study  the  texts  and  manuals  used, 
and  endeavor  thus  to  get  some  information  as  to  methods 
of  instruction.  As  the  majority  of  teachers  follow  the 
books  rather  closely,  we  shall  be  able  in  this  way  to  gain 
considerable  insight  into  the  methods  of  teaching  used 
in  the  past  and  at  the  present  time,  and  thus  to  form 
some  idea  as  to  the  educational  value  of  the  work.  In 
this  chapter  only  the  date  of  the  sources  of  the  quota- 
tions used  will  be  given,  because  these  quotations  are 
typical  of  the  system  of  teaching,  and  the  questions 
raised  are  pertinent  to  that  system  rather  than  to  any 
particular  text  or  author. 

If  you  open  almost  any  of  the  textbooks  of  physics 
or  of  natural  philosophy,  you  will  find  something  of 
this  sort  (1837)  :- 
1  Franklin,  Proc.  of  the  N.  Y.  State  Science  Teachers'  Asso.,  1907,  p.  92. 


TEXTBOOKS  OLD   AND  NEW  77 

"  i.  Natural  philosophy  is  the  science  which  treats 
of  the  powers  and  properties  of  natural  bodies,  their 
mutual  action  on  one  another,  and  the  laws  and  opera- 
tions of  the  material  world. 

"  2.  Some  of  the  principal  branches  of  Natural  Phi- 
losophy are:  Mechanics,  Pneumatics,  Hydrostatics,  Hy- 
draulics, Acoustics,  Pyronomics,  Optics,  Astronomy, 
Electricity,  Galvanism,  Magnetism,  Electromagnetism, 
and  Magneto-Electricity. 

"  3.  Matter  is  the  general  name  of  everything  that 
occupies  space  or  has  figure,  form,  or  extension. 

"  4.  There  are  seven  essential  properties  belonging 
to  all  matter,  namely :  i.  Impenetrability,  2.  Extension, 
3.  Figure,  4.  Divisibility,  5.  Indestructibility,  6.  Inertia, 
and  7.  Attraction." 

Then  follow  attempts  at  defining  these  terms,  impene- 
trability, extension,  figure,  and  the  rest. 

Or  again  (1878) :  —^  £/y6V»f 

"  i.  What  is  Science  ?  —  Science  is  classified  knowledge. 

"  A  person  may  live  for  years  among  plants,  have 
acquired  a  vast  store  of  information  concerning  them, 
know  that  this  one  grows  only  in  wet  ground,  that  another 
is  valuable  for  such  and  such  an  end,  and  that  a  third 
has  certain  form,  size,  and  color.  This  general  infor- 
mation may  be  valuable,  but  it  is  only  when  the  facts 
are  classified,  and  the  plants  grouped  in  their  respective 


78  THE  TEACHING  OF  PHYSICS 

orders,  genera,  and  species,  that  the  knowledge  becomes 
entitled  to  the  name  of  botany,  a  science. 

"  2.  What  is  Matter?  — Matter  is  anything  that 
occupies  space  or  '  takes  up  room/ 

"  There  are  many  realities  that  are  not  forms  of 
matter.  Mind,  truth,  and  hope  do  not  occupy  space; 
the  earth  and  the  raindrop  do. 

"  3.  Divisions  of  Matter.  —  Matter  may  be  considered 
as  existing  in  masses,  molecules,  and  atoms. 

"  A  clear  apprehension  of  the  meaning  of  these  terms 
is  essential  to  a  full  understanding  of  the  definition  of 
Physics,  as  well  as  of  much  else  that  follows. 

"  4.  What  is  a  Mass  ?  —  A  mass  is  any  quantity  of 
matter  that  is  composed  of  molecules. 

"  The  word  '  molar '  is  used  to  describe  such  a  collection 
of  molecules." 

Then  follows  what  are  supposed  to  be  definitions  of 
molecule,  atom,  forms  of  attraction,  forms  of  motion, 
physical  science,  physical  change,  and  physics. 

Again  (1901) :  — 

"  i.  Matter.  —  It  is  only  a  colorless  definition  of 
matter  to  say  that  it  occupies  space.  It  is  better  de- 
scribed by  its  properties,  to  which  the  next  chapter  is 
devoted.  Science  is  not  yet  able  to  tell  what  matter  is, 
but  the  balance  has  demonstrated  that  it  is  invariable 
in  amount,  whatever  form  it  may  be  made  to  assume. 


TEXTBOOKS  OLD  AND   NEW  79 

"  A  limited  portion  of  matter  is  a  body,  and  different 
kinds  of  matter,  having  distinct  properties,  are  called 
substances.  A  gold  coin,  a  drop  of  water,  air  inclosed 
in  a  vessel,  are  bodies.  Each  is  also  a  substance,  since 
it  has  properties  distinct  from  the  others. 

"  2.  Energy.  —  It  is  a  fact  of  common  observation 
that  a  body  in  motion  can  impart  motion  to  another 
body,  either  by  direct  collision  or  otherwise.  It  is 
customary  to  say  in  such  a  case  that  the  first  body 
does  work  on  the  second.  One  body  may  also  impart 
motion  to  another  by  virtue  of  its  relative  position. 
Thus,  the  weight  of  a  clock  when  wound  up  gives  motion 
to  the  pendulum  and  keeps  it  swinging  against  the  resist- 
ance of  the  air  and  of  friction.  Whenever  one  body 
changes  the  motion  or  relative  position  of  another, 
against  a  resistance  opposing  the  change,  the  first  body  is 
said  to  do  work  on  the  second.  Energy  may  be  defined 
as  the  capacity  of  doing  work.  It  is  a  grand  doctrine 
of  modern  science  that  the  energy  of  the  physical  universe 
is  conserved,  or  is  invariable  in  amount.  This  principle 
of  the  Conservation  of  Energy  will  become  clearer  when 
we  have  studied  the  various  forms  which  energy  may 
assume,  and  its  conversion  from  one  of  these  forms  into 
another. 

"3.  Physics.  —  In  its  most  general  aspect  Physics  may 
be  defined  as  the  science  of  matter  and  energy." 


8o  THE  TEACHING  OF  PHYSICS 

The  next  topics,  discussed  in  a  similar  way,  are: 
4.  Physical  Phenomena,  Theory,  Law;  5.  Experiment; 
6.  The  Properties  of  Matter ;  7.  Extension;  8.  Measure- 
ment of  Extension;  9.  Mass  and  Weight;  10.  Meas- 
urements of  Mass;  n.  Impenetrability;  12.  Porosity; 
13.  Inertia;  etc. 

Again  (1906) :  — 

"  i.  Physics  Denned.  —  Physics  treats  of  energy 
and  matter  and  their  relations  to  each  other  in  so  far 
as  there  is  no  change  in  the  identity  of  the  matter. 

"  Energy  may  be  provisionally  defined  as  that  which 
may  cause  a  change  in  matter,  and  matter  as  that  which 
occupies  space. 

"  2.  Body  and  Substance.  — A  body  is  a  distinct  por- 
tion of  matter,  as  a  nail,  a  hammer,  a  car,  a  ship,  etc. 

"  A  substance  is  a  particular  kind  of  matter,  as  iron, 
sugar,  water,  oxygen,  etc. 

"  3.  Fundamental  Quantities  in  Physics.  —  In  deal- 
ing with  energy  and  matter,  the  fundamental  quantities 
are  length,  mass,  and  time.  To  construct  an  exact  science 
it  is  necessary  to  make  accurate  measurements,  to  do 
which  requires  the  adoption  of  units  of  measurement. 

"  4.  Measurement.  —  To  measure  any  quantity  is 
to  determine  its  value  in  terms  of  a  definite  portion  of 
the  same  kind  of  quantity;  the  definite  portion  thus 
employed  is  called  a  unit  of  that  quantity." 


TEXTBOOKS  OLD   AND  NEW  8l 

The  topics  that  follow  are :  5.  Two  Systems  of  Units ; 
6.  Units  of  Length;  7.  Equivalents  of  Linear  Units; 
8.  Units  of  Mass;  9.  Equivalents  of  Units  of  Mass; 
10.  Units  of  Time,  etc.  After  denning  the  other  kinds 
of  units  and  the!  methods  of  using  them,  there  follow 
the  topics:  21.  Variation;  22.  Kinds  of  Quantities; 
23.  Ratio;  24.  Proportion;  etc. 

Once  more  (1908) :  — 

"  i.  Physics  is  the  science  of  matter  and  energy.  Each 
of  these  is  as  important  as  the  other.  We  know  nothing 
of  matter  except  through  the  agency  of  energy  and 
nothing  of  energy  except  through  the  agency  of  matter. 

"  Physics  is  one  of  the  exact  sciences.  In  its  investiga- 
tions constant  use  is  made  of  mathematics,  and  the  most 
refined  and  accurate  instruments  known  to  man  are 
often  required.  It  may  be  said  to  be  a  science  of  meas- 
urements. 

"2.  Unit  of  Measure.  —  Every  measurement  is  a 
comparison.  The  thing  with  which  the  measured 
quantity  is  compared  is  the  unit  of  measure.  If  you 
measure  the  length  of  the  table  by  your  pencil,  you  may 
say  the  table  is  ten  pencils  long.  You  have  compared 
the  length  of  the  table  with  that  of  the  pencil,  and  the 
length  of  the  pencil  is  the  unit  of  measure.  A  unit  is  the 
first  essential  in  all  measurements.  The  magnitude  of 
any  quantity  is  the  ratio  of  that  quantity  to  the  unit." 


82  THE  TEACHING  OF  PHYSICS 

This  introduction  is  followed  by  3.  Standard  and 
Legal  Units;  4.  Systems  of  Units;  5.  Fundamental  and 
Derived  Units;  6.  Absolute  Units;  7.  The  Unit  of 
Length;  8.  Definition  of  Mass;  9.  The  Unit  of  Mass; 
10.  Weight,  etc. 

This  almost  universal  habit  of  beginning  the  treatment 
of  physics  with  a  series  of  definitions  is  easily  traceable 
to  Newton,  whose  Principia  begins,  as  is  well  known,  with 
definitions  (so  called)  of  Quantity  of  Matter,  Quantity  of 
Motion,  vis  insita,  vis  impressa,  vis  centripita,  etc. 

It  is  now  a  well-known  fact  that  Newton  adopted  this 
method  of  presenting  his  researches  in  order  to  make 
discussion  of  the  results  jmpossible.  Some  of  his  earlier 
publications  on  optics  had  been  criticized  by  Hooke  and 
others,  and  he  had  been  drawn  into  quite  a  contro- 
versy about  them.  This  was  distasteful  to  Newton,  so 
he  drew  up  his  Principia  in  the  deductive  form  used  by 
Euclid,  a  form  which  admits  of  no  discussion,  once  the 
definitions  and  axioms  are  accepted.1  It  was  doubtless 
for  this  reason  that  he  calls  his  laws  of  motion  laws  or 
axioms  of  motion. 

Notwithstanding  this  fact,  writers  of  physics  texts 
have,  with  rare  exceptions,  felt  that  the  subject  must  be 
opened  with  definitions.  One  recent  text  (1902)  says: 
"  The  essential  nature  of  energy  is  unknown.  We  can 

1  Block,  La  Philosophic  de  Newton,  p.  129.     Paris,  Alcan,  1908. 


TEXTBOOKS  OLD  AND  NEW  83 

measure  its  quantity,  but  we  know  nothing  of  its  descrip- 
tive quantities.  It  may  be  provisionally  denned  as  the 
capacity  for  doing  work."  Here,  although  the  futility 
of  attempting  a  descriptive  definition  is  not  only  recog- 
nized but  expressed,  the  defining  habit  was  too  strong 
to  be  resisted.  And  the  student  must  learn  this  pro- 
visional definition,  although  both  author  and  teacher 
know  it  has  no  meaning. 

It  is  worth  noting,  in  passing,  that  the  sort  of  topics 
whose  definition  is  attempted  in  the  texts  has  changed. 
The  older  texts  "  defined  "  matter  and  the  properties 
of  matter;  the  newer  ones  define  "  physics,"  "  matter," 
"energy,"  and  then  pass  on  to  units  and  methods  of 
measurements.  This  change  is  typical  of  the  change 
that  took  place  when  natural  philosophy  was  converted 
into  physics. 

25.  General  Statements.  —  Besides  this  general  char- 
acteristic of  texts  of  beginning  with  definitions,  there 
are  several  other  traits,  which  are  common  to  almost 
all  the  books,  and  the  justification  of  which,  from  the 
point  of  view  of  teaching,  needs  discussion.  The  first 
of  these  characteristics  is  shown  in  the  following  quo- 
tations (1864) : — 

"  Liquids  transmit  pressure  equally  in  all  directions. 
This  remarkable  property  constitutes  a  very  character- 
istic distinction  between  solids  and  liquids;  since  solids 


84  THE  TEACHING   OF  PHYSICS 

transmit  pressure  only  in  one  direction,  viz.  in  the  line  of 
the  direction  of  the  force  acting  upon  them,  while  liquids 
press  equally  in  all  directions,  upward,  downward,  and 
sideways.  The  effects  of  the  practical  application  of 
this  principle  are  so  remarkable  that  it  has  been  called 
the  Hydrostatic  Paradox,  since  the  weight  or  force  of 
one  pound,  applied  through  the  medium  of  an  extended 
surface  of  some  liquid,  may  be  made  to  produce  a  pres- 
sure of  hundreds  or  even  thousands  of  pounds.  Thus, 
in  Figure  105,  A  and  a  are  two  cylinders  containing 
water  connected  by  a  pipe,"  etc. 

(1888)  "  Liquids  influenced  by  External  Pressure 
Only.  (i)  Pascal's  Law.  —  Liquids  transmit  pres- 
sure equally  in  all  directions,  and  this  acts  at  right 
angles  upon  the  surface  pressed.  The  transmission  of 
pressure  by  liquids  under  some  circumstances  is  more 
perfect  than  by  solids.  Let  a  straight  tube,  AB,  be 
filled  with  a  cylinder  of  lead,  and  a  piston  be  fitted  to 
the  end  of  the  tube,"  etc. 

(1901)  "  Laws  of  Fluids.  —  There  are  three  funda- 
mental principles  of  pressure  in  fluids  which  may  be 
called  the  laws  of  fluids  :  — 

"  I.  Fluid  pressure  is  normal  to  any  surface  on  which 
it  acts. 

"II.  Fluid  pressure  at  a  point  in  a  fluid  at  rest  is  of 
the  same  intensity  in  all  directions. 


TEXTBOOKS  OLD  AND  NEW  85 

"  III.  Fluid  pressure,  neglecting  the  weight  of  the 
fluid,  is  the  same  at  all  points  throughout  the  mass  of 
the  fluid. 

"  Fluid  pressure  is  measured  by  the  force  exerted  per 
unit  area. 

"  Illustrations.  —  Experiment.  —  Fit  accurately  to  the 
mouth  of  a  thin-walled  pint  bottle  a  close-grained  cork. 
Fill  the  bottle  full  of  water  and  then  force  in  the  cork 
by  pressure,  using  a  lever  if  necessary.  The  bottle  will 
probably  break.  Explain.  How  could  the  bursting 
force  be  estimated?  " 

(1908)  "Transmission  of  Pressure.  —  Pascal's  law 
is  as  follows:  Pressure  exerted  at  any  place  upon  a  fluid 
inclosed  in  a  vessel  is  transmitted  undiminished  in  all 
directions  to  every  part  of  the  interior  of  the  vessel. 

"  Imagine  a  box  to  be  filled  with  wheat  or  with  smooth 
bright  bicycle  balls.  Because  the  kernels  of  wheat  or 
balls  slide  over  one  another  easily  the  contents  of  the 
box  will  exert  pressure  on  its  sides  as  well  as  on  its  bot- 
tom," etc. 

This  form  of  presentation  has  been  very  common. 
It  is  very  evident  why  inductive  teaching  and  training 
in  scientific  thinking  is  impossible  with  this  kind  of 
treatment.  Yet  it  is  so  much  a  habit  of  the  adult  mind 
to  think  from  generals  to  particulars,  that  we  find  it 
cropping  out  all  through  books  that  profess  to  proceed 


86  THE  TEACHING  OF  PHYSICS 

from  particulars  to  generals.  Thus  one  of  the  recent 
texts  (1910),  in  which  the  presentation  is  mostly  from 
particular  to  general,  we  find  immediately  after  a  defini- 
tion of  "  energy  "  and  a  discussion  of  the  change  of 
"potential"  into  " kinetic"  energy,  the  following  state- 
ment: " Although  energy  is  passing  continually  through 
transformations  and  is  being  transferred  from  one  body 
to  another  around  us  on  every  hand,  no  one  has  ever 
been  able  to  prove  that  even  the  smallest  portion  can  be 
created  or  destroyed.  The  inference  is,  therefore,  that 
the  same  quantity  of  energy  is  present  in  the  universe  to-day 
I  as  existed  ages  ago ;  i.e.  that  the  quantity  of  energy 
present  in  the  universe  remains  constant.  This  is  known 
as  the  Law  of  the  Conservation  of  Energy" 

26.  Experiments  Precede.  —  It  is  gratifying  to  note 
that  several  of  the  most  recent  texts  (1908-1911)  are  de- 
cidedly inductive  in  their  method  of  presentation. 
They  teach  Pascal's  Principles,  for  example,  as  follows 
(1910):  — 

"  Transmission  of  Pressure  —  Pascal's  Law.  —  Let 
a  vessel  of  the  form  shown  in  (i),  Fig.  78,  be  filled  with 
water  to  the  point  a.  A  pressure  will  be  exerted  on 
every  square  centimeter  of  area  depending  on  the  depth  of 
that  area.  The  force  exerted  upward  against  the  shaded 
area  AB,  assumed  to  be  100  square  centimeters,  is  100  h 
grams,  if  h  is  the  depth  of  the  water  in  the  tube.  This 


TEXTBOOKS  OLD  AND  NEW  87 

force  is  entirely  independent  of  the  area  of  the  portion 
of  the  vessel  at  a.  Let  this  area  be  i  square  centimeter. 
Now,  if  i  cubic  centimeter  of  water  is  poured  into  the 
vessel,  the  depth  of  the  liquid  is  increased  i  centimeter,  and 
the  depth  of  the  surface  AB  becomes  h  -f  i  centimeters. 
The  force  now  exerted  against  AB  is  100  (h  +  i)  grams, 
i.e.  each  square  centimeter  of  AB  receives  an  additional 
force  of  i  gram.  Hence,  the  force  exerted  on  a  unit 
area  at  a  is  transmitted  to  every  unit  area  within  the 
vessel." 

This  is  followed  by  applications  to  the  hydraulic 
press,  city  water  supply,  water  motors,  hydraulic  ele- 
vators, etc.  It  will  be  noted  that  the  principle  is  nomi- 
nally derived  from  a  concrete  experience,  namely,  the 
discussion  of  the  distribution  of  pressure  of  the  water 
in  "  a  vessel  "  whose  picture  is  shown,  in  which  the 
"  force  exerted  upward  against  the  shaded  area  is  100  h 
grams)"  etc.  There  is  no  previous  discussion  of  ex- 
periences with  water  pressures  to  define  a  problem  for 
the  student  or  to  create  in  him  a  need  or  even  a  desire 
to  know  how  the  pressure  is  transmitted.  All  the  appli- 
cations are  discussed  after  the  principle  has  been  es- 
tablished from  the  concrete  (?)  laboratory  or  lecture 
experiment. 

This  method  of  proceeding  from  the  concrete  to  the 
abstract,  or  from  the  particular  to  the  general,  is  the 


88  THE  TEACHING  OF  PHYSICS 

/ 
one  usually  followed  in  those  books  that  try  to  proceed 

inductively.  Its  justification  from  the  point  of  view 
of  educational  value  is  another  of  the  topics  that  needs 
further  discussion. 

27.  Generalized  Bodies.  —  Another  characteristic  of 
all  books  in  elementary  physics  is  illustrated  in  the  fol- 
lowing statements  (1906):  "  If  a  body  possesses  energy, 
it  obtained  it  from  some  other  body  because  the  second 
body  performed  a  certain  amount  of  work  upon  the 
first  body,  and  in  performing  the  work  lost  as  much 
energy  as  the  first  body  received.  No  body  can  exert 
force  unless  it  possesses  energy.  If  a  body  possesses 
energy  because  of  some  position  or  condition  it  has  ac- 
quired by  virtue  of  work  having  been  done  upon  it,  this 
energy  is  called  potential  energy." 

This  generalized  form  of  statement  and  this  use  of 
the  indefinite  article  with  the  word  "  body  "  is  certainly 
confusing  to  young  people.  They  find  it  hard  to  visu- 
alize "  a  force  of  10,000  dynes  acting  on  a  body,"  while 
it  is  easy  for  them  to  grasp  what  is  meant  by  "  a  boy 
pulling  a  sling  shot  with  a  force  of  three  pounds." 

The  problems  in  the  newer  books  are  particular  sin- 
ners in  this  matter,  especially  since  the  introduction  of 
the  absolute  unit  of  force  and  the  mathematical  treat- 
ment of  accelerated  motion.  It  then  became  difficult, 
if  not  impossible,  to  find  real  problems  with  which  to 


TEXTBOOKS  OLD  AND   NEW  89 

"  train  the  mind  "  in  the  use  of  the  dyne  and  the  centi- 
meter per  second  per  second  ;  therefore  disembodied  prob- 
lems, such  as  "  A  force  of  5000  dynes  acts  for  10  seconds 
on  a  mass  of  250  grams,  what  momentum  is  imparted 
to  the  body?  "  had  to  be  invented. 

In  one  recent  text  (1910),  which  states  in  the  preface 
that  "The  exercises  throughout  the  book  have  been 
selected  from  concrete  cases,"  there  appear  a  number  of 
"  concrete  "  exercises  like  this  :  "  What  is  the  velocity 
of  a  body  having  uniformly  accelerated  motion  at  the 
beginning  of  the  /  th  second  ?  "  "  A  body  whose  mass  is 
20  grams  is  given  an  acceleration  of  45  cm.  per  second  per 
second.  What  is  the  required  force?"  "What  accel- 
eration will  be  given  to  a  mass  of  25  grams  by  a  constant 
force  of  500  dynes?"  etc.  This  generalized  form  of 
thinking  is  so  usual  to  physics  teachers,  that  we  find  it 
hard  to  realize  how  vague  it  is  apt  to  make  the  subject 
to  beginners. 

28.  General  Theories  Precede.  —  Another  charac- 
teristic of  many  of  the  texts  is  illustrated  by  the  fol- 
lowing quotations,  which  are  the  paragraphs  introduc- 
ing the  subjects  of  light  and  heat  in  the  books  from  which 
they  are  taken.  Thus  (1901) :  — 

"  Light,  as  distinguished  from  the  sensation  of  seeing, 
is  a  periodic  or  undulatory  disturbance  in  a  medium 
which  is  assumed  to  exist  everywhere  in  space,  even 


90  THE  TEACHING  OF  PHYSICS 

penetrating  between  the  molecules  of  ordinary  matter. 
This  medium  is  known  as  the  ether.  Light  waves  do 
not  consist  of  alternate  condensations  and  rarefactions, 
as  in  sound,  but  of  periodic,  transverse  disturbances. 
These  disturbances  are  probably  not  transverse  move- 
ments of  the  ether  itself,  but  transverse  alterations  in 
the  electrical  and  magnetic  condition  of  the  ether.  But 
whatever  may  be  the  nature  of  the  medium,  light  is  a 
wave  motion  in  it,  and  the  vibrations  are  transverse." 

Again  (1906) :  — 

"  Heat  is  molecular  kinetic  energy,  i.e.  the  energy  of 
the  vibrating  molecules  of  matter.  When  a  bullet 
strikes  an  iron  target,  its  motion  is  suddenly  stopped  and 
it  becomes  hot.  The  kinetic  energy  of  the  mass  dis- 
appears, being  changed  into  kinetic  energy  of  the  mole- 
cules. The  kinetic  theory  of  matter  affirms  that  the 
molecules  of  a  body  are  in  motion.  A  body  possesses 
energy  owing  to  this  molecular  motion  ;  the  more  rapidly 
the  molecules  move,  the  greater  is  their  energy  and  the 
hotter  is  the  body." 

Once  again  (1910):—  <- 

"  Just  as  sound  is  defined  as  undulations  in  the  air, 
or  some  other  medium,  that  produce  the  sensation  that 
we  call  '  sound,'  so  light,  in  the  same  sense,  consists  of 
undulations  or  waves  in  the  ether  that  produce  the  sensa- 
tion which  we  often  call  by  the  name  '  light.'  Not 


TEXTBOOKS  OLD  AND  NEW  91 

all  ether  waves  can  be  regarded  as  light  waves,  since 
not  all  affect  the  organ  of  sight;  but  all  ether  waves, 
from  the  longest  to  the  shortest,  transfer  energy,  and 
therefore  may  properly  be  classed  as  carriers  of  radiant 
energy. 

"  Ether  fills  all  interstellar  space  as  well  as  the  spaces 
between  the  molecules  in  bodies  of  matter.  The  ether 
is  also  of  extreme  rareness,  or  tenuity,  since  planets 
passing  through  it  suffer  no  appreciable  retardation  in 
their  orbits.  Ether  waves  possess  several  well-known 
characteristics.  They  are  transverse  waves  and  are 
propagated  with  a  definite  speed,  and  this  speed  becomes 
less  when  they  pass  through  matter  such  as  glass,  air, 
water,  etc." 

This  peculiar  mixture  of  fact  and  assumption  in  pas- 
sages of  this  sort  deserves  careful  analysis.  What  sort 
of  an  idea  does  a  student  get  when  he  is  told,  at  the  time 
of  his  first  contact  with  the  subject,  that  light  is  an  un- 
dulatory  motion  in  a  medium  which  is  assumed?  And 
what  problem  is  left  for  the  student  to  solve  in  the  sub- 
ject of  heat  when  he  is  informed  at  the  outset  that  heat 
is  molecular  kinetic  energy?  Is  there  any  motive  left 
for  further  study,  when  every  possible  question  he 
might  like  to  ask  is  thus  definitely  settled  in  advance, 
and  every  hypothesis  of  his  own  making  is  thus  nipped 
in  the  bud? 


92  THE  TEACHING  OF  PHYSICS 

This  kind  of  treatment  suggests  the  idea  that  the 
darky  preacher  must  have  been  studying  this  sort  of 
material  while  preparing  the  sermon  which  began  thus: 
"  Brederen,  dis  mawnin'  I'se  gwine  ter  define  fer  you 
the  indefinable  ;  I'se  gwine  ter  explain  ter  you  the  in- 
explicable ;  and  I'se  gwine  ter  unscrew  fer  you  the  in- 
scrutable." 

29.  Laboratory  Manuals.  —  As  far  as  method  of 
treatment  goes,  the  laboratory  manuals  are  much  more 
nearly  alike  than  are  the  texts.  Each  topic  is  treated 
under  the  heads:  Purpose,  Apparatus,  Procedure, 
Computation,  Conclusion,  or  their  equivalents,  in  strictly 
logical  order.  The  instructions  are  usually  so  detailed 
as  to  make  it  well-nigh  impossible  for  the  pupil  to  go 
wrong  or  to  raise  questions. 

The  older  manuals  made  much  of  "  verification " 
of  laws.  In  the  newer  manuals  the  purpose  of  the  ex- 
periment is  usually  stated:  "  To  find  the  specific  gravity 
of  a  liquid,"  "  To  study  the  conditions  for  equilibrium 
of  three  concurrent  forces,"  "  To  measure  E.  M.  F.  of 
cells  by  a  potentiometer,"  and  so  on. 

The  purpose  of  the  laboratory  work  is  differently 
stated  by  different  authors.  This  purpose  can,  however, 
be  already  seen  by  noting  a  series  of  experiments  like 
the  following  (1908)  "  Measure  the  resistance  of  a 
wire  by  the  method  of  substitution.  Find  the  resistance 


TEXTBOOKS  OLD  AND  NEW  93 

of  a  cell  by  the  method  of  reduced  deflection.  Find 
the  resistance  of  a  cell  by  means  of  a  voltmeter  and  an 
ammeter.  Measure  electrical  resistance  by  the  fall 
of  potential  method.  Measure  electrical  resistance  (of 
what?)  by  means  of  a  Wheatstone  bridge.  Find  the 
relative  resistance  of  different  metals,  referred  to  cop- 
per." 

Here  we  have  six  experiments  in  the  measurement  of 
the  electrical  resistance  of  various  things  by  different 
methods.  Some  of  the  recent  manuals  have  as  many 
as  nine  experiments  in  measuring  the  specific  gravity  of 
various  substances  by  different  methods.  Are  so  many 
experiments  on  one  topic  necessary  in  order  to  give  the 
topic  a  concrete  basis  for  its  comprehension  by  the  pupil, 
or  are  the  experiments  intended  really  to  familiarize 
the  pupil  with  the  technique  of  laboratory  work?  If  it 
is  the  former,  would  not  the  result  be  better  obtained 
if  the  resistances  measured  were  those  of  familiar  things, 
—  incandescent  lamps  of  various  kinds,  electric  bells 
with  the  wires  to  be  used  in  their  circuits,  telegraph 
sounders,  and  the  like,  —  instead  of  a  wire  detached 
from  life;  and  if  only  one,  or  at  the  most,  two  methods 
of  measurement  were  used?  In  other  words,  might  not 
the  study  of  the  relative  resistances  of  4,  8,  16,  and  32 
candle-power  carbon  incandescent  lamps,  and  of  40, 
60,  and  loo-watt  tungsten  lamps  on  the  same  circuit, 


94  THE  TEACHING  OF  PHYSICS 

lead  to  a  better  comprehension  of  the  importance  and 
the  function  of  electrical  resistance  in  everyday  affairs, 
than  does  the  measurement  of  the  resistance  of  never 
so  many  detached  wires  by  various  methods  never  met 
with  outside  of  a  laboratory? 

30.  Conclusions.  —  These  quotations  have  been  given 
in  order  to  emphasize  certain  characteristics  of  the  large 
majority  of  physics  textbooks,  both  old  and  new.  These 
characteristics  are:  — 

1.  The  general  prevalence  of  definitions  and  general 
statements  of  principles  at  the  beginning  of  each  topic. 
This  method  of  presentation  has  given  place  to  some 
extent  in  some  -of  the  most  recent  books  to  one  in  which 
the  topics  are  introduced  by  laboratory  or  lecture  ex- 
periments.   In  a  few  cases  we  find  topics  introduced 
by  common  experiences. 

2.  The  abstract  nature  of  the  treatment  caused  by 
discussing  not  this  or  that  particular  thing,  but  a  body, 
a  mass,  a  wire. 

3.  The   introduction   of   general    theories,    like    the 
kinetic  theory  of  matter  or  the  undulatory  theory  of 
light,  at  the  beginning  of  the  treatment  of  these  subjects. 
This  leads  to  that  peculiar  mixture  of  fact  and  assump- 
tion that  has  been  noted. 

4.  The  predominance  in  the  modern  laboratory  man- 
uals of  the  demand  for  training  in  laboratory  technique 


TEXTBOOKS  OLD  AND  NEW  95 

and  methods  of  making  refined  measurements,  wholly 
detached  from  the  problems  likely  to  arise  in  daily  life. 

It  is,  perhaps,  because  of  these  characteristics  that  the 
books  under  consideration  have  been  and  still  are  called 
"  texts."  For  a  clergyman  preaching  to  adult  minds, 
a  general  statement,  or  a  "  text,"  is  an  appropriate 
introduction  for  a  Sunday  sermon.  With  full  propriety 
he  can  set  up  his  "  text "  as  a  general  thesis  to  be  de- 
fended or  expounded,  and  then  proceed  to  its  exposition. 
But  is  this  method  of  treatment  the  most  effective  one 
to  be  found  when  the  purpose  is,  not  to  instruct  adults 
concerning  the  divine  truths  of  revelation,  but  to  train 
young  minds  into  scientific  methods  of  thinking?  This 
question  is  a  complex  and  a  difficult  one.  Before  it  can 
be  answered,  we  shall  have  to  consider  more  in  detail 
several  of  the  factors  on  which  the  answer  depends. 


PART  II 
PHYSICS  AND  DEMOCRATIC  EDUCATION 

CHAPTER  V 

THE  PEDIGREE  OF  PHYSICS 

31.  Plato.  —  As  a  first  step  toward  finding  answers  to 
the  questions  raised  in  the  last  chapter,  it  will  be  well 
to  consider  how  physical  science  has  come  to  be  what 
it  is,  and  what  it  is  at  present.  It  will,  of  course,  be 
impossible  within  the  limits  of  one  chapter  to  do  more 
than  point  out  what  seem  to  have  been  the  leading 
factors  in  its  development,  and  what  its  present  leading 
characteristics  are.  Moreover,  the  factors  and  charac- 
teristics that  are  treated  in  what  follow  are  those  which 
throw  light  on  the  use  of  physical  science  as  a  means 
of  education.  No  attempt  is  here  made  to  define 
science  as  a  whole,  nor  to  trace  its  development  in  detail. 

In  order  to  form  a  clear  idea  of  what  physical  science 
is  really  like,  we  must  disembarrass  ourselves  of  the 
tradition  that  its  foundations  were  laid  by  Plato  and 
Aristotle.  No  one  questions  the  fact  that  these  in- 
tellectual giants  of  antiquity  made  large  and  important 

96 


THE  PEDIGREE  OF  PHYSICS  97 

contributions  to  the  development  of  modern  civilization  ; 
nor  will  any  one  deny  that  it  is  possible  to  quote  from 
their  writings  vague  statements  which  may  be  inter- 
preted in  such  a  way  as  to  give  credence  to  the  claim 
that  these  philosophers  "  anticipated "  many  of  the 
notions  of  modern  physics.  But  when  we  remember 
that  science  consists  not  only  of  a  mass  of  organized 
knowledge,  but  also  of  the  method  by  which  that  or- 
ganized knowledge  was  secured,  we  must  question 
the  validity  of  the  claim  that  physical  science  is  directly 
indebted  to  any  large  extent  to  the  philosophers  of 
classical  antiquity. 

It  is,  fortunately,  not  necessary  to  discuss  in  detail 
the  philosophical  systems  of  the  Greeks  in  order  to  see 
that  their  methods  of  dealing  with  natural  phenomena 
were  totally  different  from  those  now  in  use.  No  one 
can  study  any  of  the  many  histories  of  philosophy  without 
having  this  point  made  clear.  It  will,  however,  help 
us  to  understand  modern  physics  if  we  briefly  recall 
the  leading  characteristics  of  the  teachings  of  Plato 
and  of  Aristotle. 

Plato's  system  of  philosophy  was  intended  to  give  a 
solution  of  the  problem:  how  is  it  possible  for  numerous 
individuals,  each  having  an  independent  power  of  think- 
ing, to  agree  on  anything  ?  His  solution  of  this  problem 
is  that  each  individual  possesses  "  innate  ideas/'  which 
H 


98  THE  TEACHING  OF  PHYSICS 

are  derived  from  a  previous  state  of  existence,  and  which 
are  absolutely  fixed  and  perfect.  This  body  of  innate 
ideas  make  up  the  "  real  "  world,  while  the  world  of 
phenomena  is  but  an  imperfect  and  fleeting  symbol  or 
appearance  of  this  real  world  of  immutable  celestial  ideas. 
It  is  the  presence  of  these  immutable  ideas  in  the  soul  of 
each  and  every  individual  that  makes  agreement  among 
several  apparently  independent  individuals  possible. 

Thus  when  a  customer  went  to  a  shoemaker  to  get 
a  pair  of  shoes,  the  two  "  understand  each  other  be- 
cause, although  they  are  different  '  organisms/  '  minds/ 
or  '  souls/  yet  both  have  a  '  recollection '  or  '  reminis- 
cence '  of  an  eternal  or  ( celestial '  shoe  which  each 
has  apprehended  in  a  previous  supernal  existence,  and 
of  which  all  '  terrestrial '  shoes  are  l  imitations '  or 
'  shadows.' " l 

Since  Plato's  real  world  consists  of  a  body  of  absolutely 
fixed  ideas,  it  is  a  perfectly  rigid  or  static  world.  Human 
efforts  can  produce  no  change  in  it.  Motion,  the  central 
fact  of  modern  science,  is  but  an  appearance.  Therefore, 
there  is  nothing  left  for  the  philosopher  but  to  know  this 
world  of  ideas.  Knowledge  of  it  is  obtained  by  thinking 
about  these  innate  ideas,  and  by  losing  one's  self  in 
"  celestial  contemplation  "  of  them.  Thus,  thinking  is 

1  Moore,  Pragmatism  and  its  Critics,  p.  34  (University  of  Chicago 
Press,  1910). 


THE  PEDIGREE  OF  PHYSICS  99 

the  only  function  in  our  experience  whose  activity  is 
supposed  to  be  consistent  with  the  completeness  and 
perfection  of  that  world. 

"  Thus  began  that  ever  widening  psychological  breach 
between  thought  and  the  other  activities.  Thought  soon 
becomes  a  form  or  side  or  phase  of  experience  alongside 
of  other  forms,  having  its  own  special  function,  namely, 
the  cognition  of  the  absolute  world,  which  it  exercises 
under  its  own  laws.  .  .  .  Social  agreement  and  co- 
operation at  bottom  must  now  mean  agreement  and 
cooperation  in  regaining  or  losing  the  celestial  vision. 
Our  impulses,  instincts,  desires,  emotions,  volitions,  are 
all  mere  symptoms  of  the  distortion  of  the  celestial 
vision,  or  of  attempts  at  its  restoration."  1 

Plato's  Republic  is  a  good  example  of  this  Platonic 
thinking.  In  this  "  the  family,  no  less  than  the  indi- 
vidual, is  sacrificed  to  the  state;  the  state  itself  being 
an  abstraction.  Like  the  utopists  of  modern  days,  Plato 
has  developed  an  a  priori  theory  of  what  the  state  should 
be,  and  by  this  theory  all  human  feelings  are  to  be  neg- 
lected; instead  of  developing  a  theory  a  posteriori,  i.e. 
from  an  investigation  into  the  nature  of  human  wants  and 
feelings.  .  .  .  Aristotle  saw  where  the  initial  weakness 
lay  —  in  the  disregard  of  the  individual  and  his  needs."  2 

1  Moore,  Lc.,  p.  41. 

2  Lewes,  History  of  Philosophy,  Vol.  I,  p.  269  (London,  Longmans, 
Green,  &  Co.,  3d  ed.,  1867). 


100  THE  TEACHING  OF  PHYSICS 

This  philosophy  of  Plato's  has  exercised  and  still 
exercises  a  very  powerful  influence  in  the  world.  His 
exaltation  of  the  activity  of  thinking  above  all  other 
activities  is  doubtless  one  of  the  responsible  causes  for 
the  present  belief  that  intellectual  training  and  "  mental 
discipline  "  constitute  an  education.  His  doctrine  that 
truth  is  an  eternally  fixed  idea  apart  from  and  above 
human  experience,  and  that  truth  may  be  secured  by 
contemplation  of  his  immutable  "  real  "  world  of  ideas, 
is  distinctly  at  variance  with  the  present  ideas  of  science. 
Platonic  love  is  generally  recognized  as  an  idea  that 
runs  counter  to  deep-seated  traits  of  human  nature, 
while  this  Platonic  thought  still  flourishes;  yet  both 
neglect  the  profound  fact  that  humanity  possesses  emo- 
tions and  feelings  as  well  as  powers  of  thought.  How 
much  of  our  present  educational  system  is  the  result  of 
Platonic  thought,  derived  from  a  contemplation  of  fixed 
and  abstract  ideas  of  what  children  should  be?  And 
how  much  is  based  on  a  scientific  study  of  what 
children  actually  are  ?  This  is  a  problem  of  rich  content 
for  some  historian  of  education. 

32.  Aristotle.  —  Aristotle's  physics  is  thus  character- 
ized by  the  most  recent  critic  of  it: 1  "  It  is  interesting 
in  this  respect  to  compare  the  Aristotelian  theory  of 

1  Henri  Bergson,  Creative  Evolution,  Engl.  Tr.  by  Mitchell,  p.  228 
(New  York,  Holt,  1911). 


THE  PEDIGREE  OF  P'HSICS  loi 

the  fall  of  bodies  with  the  explanation  furnished  by 
Galileo.  Aristotle  is  concerned  solely  with  the  concepts 
'  high  '  and  '  low/  '  own  proper  place  '  as  distinguished 
from  '  place  occupied/  '  natural  movement '  and  '  forced 
movement';  the  physical  law  in  virtue  of  which  the 
stone  falls  expresses  for  him  that  the  stone  regains  the 
'  natural  place  '  of  all  stones,  to  wit,  the  earth.  The 
stone,  in  his  view,  is  not  quite  stone,  so  long  as  it  is 
not  in  its  normal  place;  in  falling  back  into  this  place  it 
aims  at  completing  itself,  like  a  living  being  that  grows, 
thus  realizing  fully  the  essence  of  the  genus  stone.  .  .  . 
We  know  what  kind  of  physics  grew  out  of  this, 
and  how,  for  having  believed  in  a  science  unique  and 
final,  embracing  the  totality  of  the  real  and  at  one  with 
the  absolute,  the  ancients  were  confined,  in  fact,  to  a 
more  or  less  clumsy  interpretation  of  the  physical  in  terms 
of  the  vital.  ...  The  ancients  did  not  ask  why  na- 
ture submits  to  laws,  but  why  it  is  ordered  according 
to  genera." 

Again  (p.  330) :  "  The  ancient  science  thinks  it  knows 
its  object  sufficiently  when  it  has  noted  of  it  some  privi- 
leged moments  (as  the  stone  when  at  rest  on  the  earth), 
whereas  modern  science  considers  the  object  at  any  mo- 
ment whatever.  .  .  .  The  forms  or  ideas  of  Plato  or  of 
Aristotle  correspond  to  salient  moments  in  the  history  of 
things  —  those  in  general  that  have  been  fixed  by  Ian- 


102   •«''•  'THE  TEACHING  OF  PHYSICS 

guage.  .  .  .  We  may  say,  then,  that  our  physics  differs 
from  that  of  the  ancients  chiefly  by  the  indefinite  break- 
ing up  of  time." 

From  the  point  of  view  of  modern  science,  the  leading 
characteristics  of  the  Greek  philosophies  were:  i.  Their 
taking  one  particular  aspect  of  a  phenomenon  as  alone 
characteristic  and  descriptive  of  it;  whence  2.  Their 
classification  of  phenomena  into  genera  and  species  in 
accordance  with  the  aspects  selected  as  characteristic; 
3.  Their  insistence  upon  the  finality  and  immutability 
of  innate  ideas.  Because  these  fundamental,  general 
characteristics  are  so  different  from  those  of  modern 
physics,  it  seems  justifiable  to  conclude  that  modern 
physics  is  not  directly  descended  from  the  Greek  phi- 
losophy. 

This  conclusion  is  further  strengthened  by  the  fact  that 
during  the  Middle  Ages,  one  of  the  greatest  stumbling 
blocks  to  the  progress  of  modern  physics  was  the  scho- 
lastic philosophy,  which  developed  from  hair-splitting 
discussions  of  the  meaning  of  the  writings  of  Aristotle. 

33.  Art  Precedes  Science.  —  If,  then,  physical  science 
is  not  the  outcome  of  the  Greek  philosophy,  whence  did 
it  come?  The  answer  to  this  question  is  contained  in 
the  recognized  fact  that  the  manual  arts  have  always 
developed  before  science.  As  has  often  been  pointed  out, 
the  Egyptians  could  not  have  built  the  pyramids  unless 


THE  PEDIGREE  OF  PHYSICS  103 

they  were  acquainted  with  the  use  of  the  "  mechanical 
powers. "  Yet  the  scientific  treatment  of  these 
"  powers  "  began  with  Archimedes'  treatment  of  the 
lever,  and  may  be  regarded  as  not  yet  having  attained 
its  utmost  perfection.  The  Israelites  knew  that  they 
could  not  make  "  bricks  without  straw  " ;  yet  it  is  only 
recently  that  the  "  scientific  "  reason  for  this  has  been 
evolved.  The  steam  engine  was  a  highly  perfected 
machine  before  thermodynamics'  became  a  science;  and 
music  was  a  well-developed  art  before  Helmholtz  wrote 
his  Sensations  of  Tone. 

The  detailed  study  of  the  history  of  science  from  this 
point  of  view  is  a  fascinating  occupation,  but  beyond 
the  scope  of  this  book.  We  find  the  savage  pursuing  a 
crude  science  in  his  efforts  to  control  his  physical  en- 
vironment and  to  foresee  the  results  that  might  be 
expected  to  follow  from  various  combinations  of  cir- 
cumstances. Impelled  by  a  very  real  need  —  hunger  — 
we  may  imagine  him  thinking  over  the  various  facts 
in  his  possession  regarding  food;  then  selecting  fish  as 
the  means  of  meeting  his  need  with  the  "  least  action  "; 
then  making  a  plan,  i.e.  framing  an  hypothesis  as  to 
how  to  secure  the  fish;  and  finally  putting  his  hy- 
pothesis to  the  test  of  experiment.  If  he  caught  the 
fish  and  his  hypothesis  was  verified,  we  can  imagine  him 
telling  his  comrades  that  he  had  discovered  the  "  truth  " 


104  THE  TEACHING  OF  PHYSICS 

about  fishing;  or,  at  least,  he  might  claim  that  he  had 
found  an  "  expedient  "  way  of  thinking  about  fish  and 
the  other  related  factors  in  his  physical  world. 

The  high  thinkers  among  the  Greeks  and  Romans 
did  not  apply  this  method  of  solving  the  problems 
of  their  physical  surroundings  very  extensively,  because 
it  was  not  their  function  in  society  to  take  part  in  the 
industrial  activities  of  the  times.  These  functions 
belonged  to  the  slaves  —  the  philosophers  were  there  to 
"  just  think  "  Platonic  thought. 

The  Romans,  however,  must  have  solved  many  political 
problems  in  the  scientific  way.  Their  civil  law  was 
constantly  changing  to  meet  the  exigencies  of  new  situa- 
tions, and  their  magnificent  achievements  in  political 
organization  could  hardly  have  been  possible  if  they 
had  not  been  skillful  in  finding  the  "  most  expedient  " 
methods  of  dealing  with  concrete  political  and  social 
situations. 

34.  Development  of  Industry.  —  For  science,  the 
most  important  fact  from  the  Middle  Ages  is  the  gradual 
development  of  industry  first  by  serfs,  then  by  freedmen. 
Industry,  not  politics,  was  one  of  the  potent  factors  that 
brought  about  the  change  from  serfs  to  freedmen.  When 
overproduction  began,  trade  and  commerce  were  insti- 
tuted. Since  those  were  times  of  uncertainty,  the  men 
interested  in  industry  and  trade  organized  the  guilds 


THE   PEDIGREE   OF  PHYSICS  105 

and  then  the  towns  for  the  mutual  protection  of  common 
interests,  —  the  beginning  of  the  modern  spirit  of  co- 
operation. Then  feudal  lords  and  the  fiefs  were 
swallowed  up  in  the  formation  of  kingdoms,  which  were 
larger  units  offering  better  protection  for  the  interests 
of  industry  and  commerce.  Here  again,  the  industrial 
and  commercial  interests  were  powerful  factors  in 
bringing  about  the  change. 

According  to  Adams: 1  "  The  various  lines  of  growth 
which  began  an  increasing  activity  from  the  Crusades, 
and  which  led  out  from  the  Middle  Ages  into  modern 
history,  were  dependent  for  their  accelerated  motion, 
for  immense  reenforcement,  if  not  for  actual  beginning, 
upon  the  rapidly  developing  commercial  activities  of 
the  time." 

Again: 2  "  The  increase  of  commerce  and  the  develop- 
ment of  cities  becomes  the  rise  of  the  third  estate  into  a 
position  of  power.  This  is  a  fact  of  utmost  importance 
in  the  general  history  of  civilization,  because  this  progress 
once  begun  in  reality  never  ceased ;  and  in  our  own  time 
is  characterized  by  the  practical  absorption,  economi- 
cally and  politically,  of  the  other  two  estates  into  the 
third.  At  the  beginning  of  the  Middle  Ages,  the  first  es- 
tate —  the  clergy  — and  the  second  estate —  the  nobles— 

1  Adams,  Civilization  during  the  Middle  Ages,  p.  280  (New  York, 
Scribner,  1900).  2  Ibid.,  p.  305. 


106  THE  TEACHING  OF  PHYSICS 

controlled  everything.  With  the  growth  of  commerce 
this  began  to  be  changed.  The  ready  money  of  the 
merchant  was  as  effective  a  weapon  as  the  sword  of  the 
noble  or  the  spiritual  arms  of  the  church.  Speedily  also 
the  men  of  the  cities  began  to  seize  upon  one  of  the 
weapons  which  had  been  the  exclusive  possession  of  the 
church  and  one  of  the  main  sources  of  its  power  — 
knowledge  and  intellectual  training.  With  these  two 
weapons  —  wealth  and  knowledge  —  the  third  estate 
forced  its  way  into  influence." 

Again: *  "  The  kings  sought  only  political  power  and 
did  not  care  to  preserve  serfdom,  until,  too  late,  they 
saw  that  complete  industrial  freedom  tended  toward  a 
democracy  that  would  be  as  inimical  to  royalty  as  the 
feudal  aristocracy  had  been.  Among  the  townsmen 
there  was  no  strong  desire  for  municipal  liberty,  pro- 
vided the  economic  arrangements  could  be  adapted  to 
the  needs  of  commerce  without  political  independence. 
Self-government  was  only  an  expedient  to  which  the 
merchants  had  been  compelled  to  resort  in  order  to  free 
themselves  from  the  sovereignty  of  the  lords.  It  is  a 
fallacy  to  read  back  into  the  consciousness  of  the  burghers 
who  were  struggling  for  the  right  of  self-government  a 
desire  for  independence  for  its  own  sake.  In  the  be- 

1  Forrest,  Development  of  Western  Civilization,  p.  212  (University 
of  Chicago  Press,  1907). 


THE  PEDIGREE  OF  PHYSICS  107 

ginning  independence  was  desired  for  practical  reasons 
only." 

In  its  earlier  stages  the  industrial  movement  was  a 
necessity  in  order  to  supply  the  necessities  of  life  and 
the  muniments  of  war.  In  the  course  of  time,  as  politi- 
cal conditions  became  more  stable,  the  human  needs 
which  it  was  called  upon  to  satisfy  became  more  diversi- 
fied; the  intellectual  and  artistic  cravings  of  the  mind 
began  to  demand  satisfaction,  and  the  technique  of  in- 
dustry had  to  be  enriched  to  meet  the  situation. 
Cathedrals  and  castles  were  built,  Gothic  architecture 
was  developed,  and  ornaments  in  bronze  and  stone  were 
wrought  out  with  a  mechanical  skill  that  has  not  been 
surpassed. 

It  is  not  difficult  to  see  why  industry  and  commerce 
were  the  chief  lines  along  which  marked  progress  was 
made  in  the  Middle  Ages.  During  the  thousand  years 
that  intervened  between  the  fall  of  the  Roman  Empire 
and  the  publication  of  Copernicus's  epoch-making 
work  (1543),  all  abstract  thinking  was  controlled  from 
Rome.  The  doctrines  of  the  church  demanded  an  ascetic 
and  devout  life  here,  and  a  blind  faith  in  the  doctrine  of 
salvation  by  faith  alone  and  that  of  the  infallibility  of 
the  Pope.  Industry  and  commerce  were  the  only  fields 
of  activity  in  which  no  Roman  doctrine  blocked  the  way 
of  progress,  and  which  were  even  encouraged  by  the 


108  THE  TEACHING  OF  PHYSICS 

church  in  its  teachings  concerning  the  worth  of  the 
individual  and  the  dignity  of  labor.  But  in  spite  of  its 
efforts  to  suppress  thought,  the  church  finally  started, 
unwittingly,  to  be  sure,  the  new  age,  when  it  called  upon 
Christendom  to  unite  in  the  Crusades  and  drive  the 
infidel  from  the  Holy  Sepulchre. 

The  Crusades  opened  the  eyes  of  Europe  to  the  fact 
that  there  were  many  interesting  things  to  do  in  this 
world  beside  contemplating  a  problematic  future  life. 
During  the  Crusades  (1092-1200)  the  industrial  and 
commercial  classes  rose  rapidly  in  importance  because 
of  the  business  which  the  Crusades  made.  In  the 
so-called  Renaissance  we  see  the  interest  in  worldly 
things  breaking  forth  with  passionate  eagerness,  leading 
men  to  seek  information  about  this  world  and  its  people, 
even  in  the  classics.  This  eagerness  for  information 
about  the  world  made  necessary  the  invention  of  print- 
ing and  the  establishment  of  the  first  newspaper  (1505); 
it  inspired  the  voyages  of  discovery  by  Columbus, 
Magellan,  and  the  rest  ;  and  the  returns  that  came  from 
this  invention  and  these  voyages  created  new  enthusiasm 
for  the  life  here  below  and  an  increased  desire  for  a 
better  knowledge  of  nature  and  her  ways. 

35.  The  Method  of  Industry.  —  For  the  student  of 
the  history  of  science,  there  are  several  important  points 
to  be  noted  in  this  development.  In  the  first  place, 


THE  PEDIGREE  OF  PHYSICS  109 

the  process  by  which  it  was  accomplished  was  this: 
some  human  need,  desire,  longing,  or  aspiration  made 
itself  felt,  whereby  a  real  problem  was  denned,  —  a 
problem  that  would  not  lie  down  and  keep  quiet  until 
the  need  that  called  it  into  existence  was  satisfied.  The 
solution  was  found  by  first  studying  concrete  things, 
then  forming  a  plan  of  action  which  seemed  expedient 
under  the  circumstances,  and  then  testing  the  plan  by  a 
process  of  adaptation  of  means  to  end,  of  approximation, 
and  of  experimentation. 

In  the  second  place,  the  solution  of  one  problem  reacted 
to  stimulate  new  needs  and  desires;  and  these,  in  turn, 
defined  new,  more  refined,  and  more  difficult  problems. 
Thus  it  has  gone  from  one  need  to  one  problem  to  new 
needs  to  more  problems,  thence  to  additional  higher 
needs,  whence  more  problems;  and  so  on,  ad  infinitum. 
Because  of  this  the  process  was  a  vital  one,  capable  of 
growth. 

In  the  third  place,  the  success  of  this  great  upward 
movement  of  industry  and  commerce  was  due  to  the 
fact  that  they  were  able  to  "  deliver  the  goods  "  that 
were  needed  to  satisfy  the  human  desires  that  called 
them  into  being.  They  were  able  to  produce  tangible 
results  which  everybody  wanted  and  could  comprehend, 
and  whose  "  expediency  "  no  one  could  deny. 

In   the   fourth  place   the   discoveries  and  successes 


110  THE  TEACHING  OF  PHYSICS 

achieved  by  this  method  of  solving  problems  were  so 
concrete,  so  impelling,  so  undeniable,  that  even  the 
infallible  church  had  to  succumb.  Because  of  this,  large 
bodies  of  men  came  to  rely  on  the  method  as  the  one 
method  that  was  capable  of  yielding  dependable  and  de- 
monstrable results,  so  that  it  came  into  common  use  on  a 
large  scale  among  the  commercial  and  industrial  classes. 
When  large  bodies  of  men  had  thus  become  accustomed 
to  thinking  in  this  way,  the  time  was  ripe  for  the  ex- 
tension of  the  method  to  the  solution  of  more  general 
and  more  abstract  problems.  Then  it  was  that  modern 
physics  proper  began.  The  fact  that  physics  did  not 
begin  until  commerce  and  industry  were  well  developed 
is  one  of  the  fundamentally  important  facts  to  remember 
when  studying  the  problem  of  how  to  use  physics  for 
purposes  of  general  education. 

As  a  further  example,  consider  how  the  Crusades 
created  a  demand  for  a  means  of  travel  to  the  Holy  Land. 
The  first  Crusade,  1097,  went  entirely  by  land,  while 
the  third,  1187,  went  largely  by  sea.  Shipbuilding  had 
expanded  in  the  interim  to  meet  the  demand,  and  it  has 
flourished  ever  since  because  it  produced  the  tangible 
results  that  the  people  wanted.  And  who  can  estimate 
the  indebtedness  of  the  present  civilization  to  this  same 
industry? 

Every  one  will  agree  to  the  fact  that  the  shipbuilding 


THE.  PEDIGREE  OF  PHYSICS  m 

industry  has  contributed  largely  to  the  growth  of  civili- 
zation. Still,  there  are  many  who  will  say  :  "  Yes,  but 
it  was  the  '  idea  '  of  ship  that  created  the  industry,  and 
this  idea  is  '  innate '  in  mankind.  Has  not  Charon 
been  ferrying  souls  across  the  Styx  from  all  eternity?  " 
If  this  is  true,  why  were  not  the  first  ships  electric-lighted 
ocean  greyhounds?  No,  it  was  reserved  for  men  to 
discover  by  a  long  process  of  trial  and  error,  —  of  adap- 
tation, approximation,  and  experiment, — what  the  "most 
expedient  "  form  of  ship  was.  And  this  "  form  "  is  not 
immutable,  but  changes  and  develops  to  keep  pace  with 
the  industrial  and  commercial  needs  on  the  one  hand 
and  human  desire  and  fancy  on  the  other. 

No  one  at  present  can  fail  to  recognize  the  fact  that  we 
are  now  living  in  an  industrial  and  commercial  age  —  for 
the  industrial  movement,  which  began  when  it  became 
socially  permissible  for  a  freeman  to  engage  in  these 
activities,  has  continued  to  advance  with  a  positive 
acceleration  ever  since.  It  has  supplied  the  concrete 
foundation  of  our  present  social  order  and  was  a  veri- 
table father  to  modern  physics.  The  fact  that  physics 
is  a  direct  lineal  descendant  from  industry  has  important 
bearings  on  the  pedagogical  problem. 

36.  Germanic,  Industry.  —  This  industrial  and  com- 
mercial development  is  the  work  of  the  Germanic 
races;  and  its  marvelous  success  is  due  to  the  method 


112  THE  TEACHING   OF  PHYSICS 

of  thinking  which  they  alone  have  known  how  to  use 
with  all  its  vigor.  Men  have  always  solved  the  prob- 
lems that  nature  thrusts  upon  them  by  a  more  or  less 
crude  use  of  the  method.  But  it  was  reserved  for  the 
Germanic  races  to  apply  it  with  success  to  industry, 
science,  and  abstract  thinking.  This  was  because 
the  Germanic  thinking  differed  from  that  of  classical 
antiquity  in  several  fundamental  points.  These  points 
are  thus  explained  by  Chamberlain:1  "The  Greek 
made  few  observations,  and  those  never  without  bias; 
he  was  not  endowed  with  the  long-enduring  patience 
which  is  necessary  in  order  to  make  any  great  discovery." 

"  The  whole  secret  of  making  discoveries  lies  in  letting 
nature  speak.  To  do  this  requires  great  self-control,  a 
characteristic  which  the  Greeks  did  not  possess.  The 
weight  of  their  genius  lay  in  their  creative  imagination; 
the  weight  of  ours  lies  in  our  receptivity." 

"  The  great  work  of  laborious  discovery  has  a  deadly 
enemy:  the  know-it-all.  With  Aristotle  a  problem  is 
hardly  stated  before  its  answer  is  given.  ...  We  see, 
therefore,  why  the  work  of  discovery  was  so  long  in  be- 
ginning." 

"  All  systematization  and  theorizing  is  a  fitting  to- 

1  Chamberlain,  Die  Grundlagen  des  Neunzehnten  Jahrhunderts,  pp. 
760  sq.  (4th  ed.,  Miinchen,  Bruchman,  1903).  An  English  translation 
has  just  appeared  (New  York,  Lane,  1911). 


THE  PEDIGREE  OF  PHYSICS  113 

gather,  an  adaptation,  which,  while  as  accurate  as  pos- 
sible, is  never  wholly  without  error.  The  Greek  did  not 
know  this.  Unexcelled  as  a  creator  of  form,  he  demanded 
perfection  and  complete  rounding  out  in  science  as  well; 
thereby  he  sealed  for  himself  the  door  by  which  men  may 
enter  into  a  knowledge  of  nature.  .  .  .  We  Germans  are 
engineers  rather  than  architects.  We  also  know  how  to 
create  forms;  yet  our  aim  is  not  the  beauty  of  the  thing 
formed,  nor  yet  a  form  perfect  and  giving  final  satis- 
faction to  the  human  mind,  but  rather  the  establishment 
of  a  proviso  which  makes  possible  the  collection  of  new 
data  and  thereby  a  wider  knowledge.  .  .  .  Our  scientific 
process  is  a  denial  of  the  absolute." 

The  Germanic  attitude  toward  nature  may  then  be 
characterized  as  one  of  desire  to  learn  and  possess;  it 
lays  weight  on  the  utility  of  the  result  in  satisfying 
human  needs,  and  is  content  to  use  approximations 
and  provisional  forms,  provided  only  that  they  enable 
us  to  accomplish  this  purpose.  Germanic  science  seeks 
to  discover  laws,  —  that  is,  constant  relations  between 
variable  quantities,  —  and  it  does  this  by  experiment 
and  approximation.  It  is,  therefore,  not  absolute,  but 
relative;  not  perfect,  but  approximate;  not  dogmatic, 
but  open-minded. 

What  Aristotle  would  call  the  "  quintessence  "  of  this 
great  industrial  development  has  been  pointed  out  by 


114  THE  TEACHING  OF  PHYSICS 

Carlyle  in  his  Review  of  the  Corn  Law  Rhymes  in  the 
following  words : l  "  Nay  it  appears  to  us  as  if  in  this 
humble  Chant  of  the  Village  Patriarch  might  be  traced 
rudiments  of  a  truly  great  idea;  great,  though  all  un- 
developed. The  Rhapsody  of  '  Enoch  Wray '  is,  in  its 
nature  and  unconscious  tendency,  Epic;  a  whole  world 
lies  shadowed  in  it.  What  we  might  call  an  inarticulate, 
half-audible  Epic  !  The  main  figure  is  a  blind  aged  man; 
himself  a  ruin  and  encircled  with  the  ruin  of  a  whole  Era. 
Sad  and  great  does  that  image  of  a  universal  Dissolution 
hover  visible  as  a  poetic  background.  Good  old  Enoch  ! 
He  could  do  so  much  ;  was  so  wise,  so  valiant.  No 
Ilion  had  he  destroyed;  yet  somewhat  he  had  built  up : 
where  the  Mill  stands  noisy  by  its  cataract,  making 
corn  into  bread  for  men,  it  was  Enoch  that  reared  it, 
and  made  the  rude  rocks  to  send  it  water;  where  the 
mountain  Torrent  now  boils  in  vain,  and  is  mere  passing 
music  to  the  traveler,  it  was  Enoch's  cunning  that 
spanned  it  with  that  strong  Arch,  grim,  time-defying. 
Where  Enoch's  hand  or  mind  has  been,  Disorder  has 
become  Order;  chaos  has  receded  some  little  hand- 
breadth,  had  to  give  up  some  new  handbreadth  of  his 
ancient  realm. 

"  Rudiments  of  an  Epic,  we  say;   and  of  the  true  Epic 
of  our  Time,  —  were  the  genius  but  arrived  that  could 
1  Carlyle,  Essays,  Vol.  Ill,  p.  161  (New  York,  Scribner). 


THE  PEDIGREE  OF  PHYSICS  115 

sing  it !  Not '  Arms  and  the  Man' ;  '  Tools  and  the  Man/ 
that  were  now  our  Epic.  What  indeed  are  tools,  from 
the  Hammer  and  Plummet  of  Enoch  Wray  to  this  Pen 
we  now  write  with,  but  Arms,  wherewith  to  do  battle 
against  Unreason  without  or  within,  and  smite  in 
pieces  not  miserable  fellow  men,  but  the  Arch-Enemy 
that  makes  us  all  miserable;  henceforth  the  only  legiti- 
mate battle !  " 

Since  the  "  genius  that  could  sing  it "  has  not  yet 
arrived,  it  is,  unfortunately,  not  possible  to  study  this 
"  Epic  of  our  Time  "  as  much  in  detail  as  would  be  de- 
sirable for  teachers  of  science.  It  is,  however,  possible 
to  gain  some  insight  into  the  reason  why  "  Good  old 
Enoch  could  do  so  much,"  before  a  "  poetic  background 
of  universal  Dissolution  "  and  "  encircled  with  the  ruin  of 
a  whole  Era."  Is  not  his  being  "  so  wise,  so  valiant " 
that  "  where  his  hand  or  mind  has  been,  Disorder  has 
become  Order  "  due  in  large  measure  to  the  fact  that 
the  method  of  thinking  which  he  used  when  he  made 
"  the  rude  rocks  send  it  water  "  was  the  only  method  that 
has  ever  proved  effective  when  man  wishes  to  control 
Nature  and  be  able  to  predict  the  results  of  her  processes  ? 
Did  he  sit  still  and  lose  himself  in  contemplation  of 
"  celestial "  rocks  and  "  immutable  "  water?  Did  he  re- 
tire to  his  inner  consciousness  and  just  think  Platonic 
thought  until  convinced  of  the  "  truth  "  of  Bradley 's 


Il6  THE  TEACHING  OF  PHYSICS 

famous  phrase  "  Nothing  real  can  move  "  ?  Not  he. 
There  was  a  human  need  to  be  satisfied  by  grinding 
corn;  he  realized  the  need  and  longed  to  serve  humanity 
by  helping  it  to  satisfy  its  hunger.  So  he  studied  the 
situation,  formed  a  plan  of  action  that  seemed  "  ex- 
pedient "  under  the  circumstances,  and  then  put  his 
plan  to  the  test  of  experience. 

37.  The  Parents  of  Physics.  —  As  has  been  stated, 
the  conclusion  that  seems  warranted  from  the  preceding 
discussion  is  that  Germanic  industry  was  the  father  of 
modern  physics.  On  the  other  hand,  the  father  of  the 
ancient  science  was  a  very  different  sort  of  being.  For 
while  Germanic  industry  is  cooperative,  democratic, 
and  not  afraid  of  work,  the  parent  of  ancient  science 
was  exclusive,  aristocratic,  and  unwilling  to  soil  his 
hands  in  work.  As  a  result  of  their  ancestry,  modern 
physics  is  cooperative,  democratic,  and  industrious, 
while  ancient  physics  is  exclusive,  aristocratic,  and  lazy. 

But  though  the  classic  and  the  modern  physics  have 
different  fathers,  they  have  the  same  mother.  The 
Greeks  recognized  wonder  as  the  mother  of  the  sciences. 
In  like  manner,  the  moderns,  as  Dewey  puts  it,  consider 
that  "  wonder  is  not  only  the  originator,  but  it  is  the 
continuer  of  science.  Wonder  is  the  emotional  outgoing 
of  the  mind  toward  this  universe.  It  is  the  sole  spring 
which  can  take  a  man  beyond  his  subjective  states,  and 


THE  PEDIGREE  OF  PHYSICS  117 

put  him  in  that  active  relation  to  the  world  which  is  the 
sole  condition  of  getting  at  its  meaning.  But  it  is  no 
less  true  that  wonder  is  the  cause  of  all  growth,  of  all 
increase  in  knowledge.  Wonder  as  the  outgoing  activity 
of  the  mind,  necessarily  requires  a  surrender  of  all 
purely  subjective  and  selfish  interests,  and  the  devotion 
of  one's  self  to  the  object  wholly  for  the  sake  of  the 
latter." 1 

Thus  ancient  physics  is  related  to  modern  physics 
because  of  the  fact  that  both  were  mothered  by  that 
deep-seated  human  emotion  of  wonder.  If  her  first 
marriage  to  that  exclusive  and  aristocratic  laziness  of 
the  ancients  resulted  in  offspring  who  could  not  "sur- 
render all  purely  subjective  interests,"  but  preferred 
thinking  Platonic  thought  to  working  at  the  world's 
work,  her  second  marriage  to  the  cooperative  and  demo- 
cratic industry  of  the  Germanic  races  must  have  more 
than  consoled  her  for  her  former  misfortune ;  for  modern 
physics  is  a  son  of  whom  any  mother  might  well  be 
proud. 

38.  The  Renaissance.  —  No  objection  will  be  raised 
against  this  analysis  of  the  history  of  industry,  since  all 
recognize  its  origin  and  its  present  importance.  Many 
will,  however,  demur  at  the  conclusion  that  modern 
physics  is  the  son  of  democratic  Germanic  industry  and 

1  Dewey,  Psychology,  p.  303  (New  York,  Harper,  1897). 


Il8  THE  TEACHING  OF  PHYSICS 

not  of  aristocratic  Platonic  thought.  Every  history  of 
physics  and  every  history  of  philosophy  treats  the  subject 
in  chronological  order,  first  describing  the  Greeks  and 
their  works  and  then  passing  on  to  modern  times,  as 
though  there  were  no  discontinuity,  no  break  in  the 
development.  According  to  the  story,  Greek  science 
was  "  preserved  "  by  the  Arabians  through  the  "  dark 
ages  "  and  brought  back  into  Europe  during  the  Crusades 
and  the  Renaissance.  Was  not  the  period  from  1200 
to  1400  A.D.  called  Renaissance  because  its  chief  function 
was  the  re-discovery  of  the  works  of  the  ancients  ?  And 
when  these  "  preserved  "  works,  which  are  "  absolute  " 
and  "  immutable "  and  which  therefore  contain  the 
quintessence  of  all  wisdom,  were  finally  uncorked  and 
freely  imbibed  in  Europe,  the  moderns  got  so  full  of  the 
ancient  spirit  that  they  have  devoted  themselves  ever 
since  to  an  effort  to  reproduce  more  of  it. 

39.  Archimedes.  —  All  this  may  be  so  as  far  as  art 
and  literature  and  the  "  humanities "  are  concerned, 
but  nothing  can  be  less  true  than  this  as  far  as  physical 
science  goes.  The  fact  that  Archimedes  discovered  the 
law  of  the  lever  and  the  principle  of  equilibrium  of  float- 
ing bodies  is  the  mainstay  of  the  idea  that  modern 
physics  is  a  direct  descendent  of  the  physics  of  Aristotle. 
But  both  of  these  principles  are  static,  while  modern 
physics  is  dynamic.  He  solved  the  lever  problem  by 


THE  PEDIGREE  OF  PHYSICS  119 

means  of  an  artistic  sense  of  symmetry  —  the  equal 
weights  at  equal  distances  from  the  fulcrum  are  in 
equilibrium  because  then  the  whole  system  is  symmetrical 
with  respect  to  the  axis ;  under  these  conditions  we  can 
see  no  reason  why  it  should  turn  one  way  rather  than  the 
other;  therefore  it  must  remain  at  rest.  Archimedes 
also  gives  rules  for  finding  the  centers  of  gravity  of 
numerous  things  —  not  real  bodies,  however,  but  geo- 
metrical figures,  triangles,  squares,  spheres,  cylinders, 
and  the  like. 

In  the  case  of  the  floating  bodies  he  comes  nearer  to 
the  modern  method  of  procedure.  In  this  case,  however, 
his  problem  was  a  commercial  one,  namely,  to  find  out  if 
the  silver  smith  had  cheated  the  king.  In  this  case  he 
actually  tried  an  experiment,  —  that  of  taking  a  bath,  — 
but  history  fails  to  record  whether  he  ever  repeated  the 
experiment  or  not.  He  is  said  to  have  weighed  the 
crown  to  the  discomfiture  of  the  silversmith,  but  this  is 
almost  the  only  case  on  record  of  measurements  having 
been  made  by  a  Greek  philosopher ;  and,  as  has  been  re- 
marked, this  was  done  in  the  interests  of  industry. 

We  do  find  Ptolemy  at  Alexandria  making  measure- 
ments of  the  angles  of  incidence  and  refraction  of  light 
passing  from  air  to  water.  But  he  was  unable  to  do 
anything  with  his  results  when  he  had  them.  The 
"  immutable  idea  "  that  was  needed  was  not  "  innate  " 


120  THE  TEACHING  OF  PHYSICS 

in  him :  he  had  failed  to  notice  "  celestial  "  refraction  in 
his  "  previous  existence."  It  remained  for  Snell  (1621), 
of  Germanic  tribe,  to  find  the  "  form  "  into  which  the 
measurements  of  Ptolemy  might  be  fitted;  and  he  did 
it  by  a  method  of  trial  and  error,  or  adaptation,  approxi- 
mation, and  experiment. 

The  more  one  studies  the  methods  used  by  ancient 
physics,  the  greater  appears  to  be  the  disparity  between 
them  and  those  of  modern  physics.  The  physics  of 
Aristotle  was  studied  assiduously  in  the  universities 
during  the  entire  Renaissance  and  down  to  Galileo's 
time  (1200-1550),  yet  with  the  exception  of  those  pages 
devoted  to  Roger  Bacon's  protest  against  Aristotelian 
methods,  the  histories  of  physics  have  nothing  but  blank 
pages  descriptive  of  this  era.  ^  And  when  Galileo  ap- 
peared on  the  scene,  his  first  dramatic  act  was  to  refute 
forever  Aristotle's  dogmas  about  falling  bodies  by 
dropping  a  cannon  ball  and  a  bomb  from  the  top  of  the 
leaning  tower  of  Pisa.  From  that  day  the  influence  of 
Aristotle  has  steadily  declined ;  but  that  it  is  not  yet  all 
gone  is  shown  by  the  appearance  in  recent  books  of  such 
phrases  as  "  light  is  a  wave  motion  in  a  medium  that  is 
assumed." 

40.  Galileo  and  Guttenberg.  —  As  a  reward  for  his 
impudence  in  daring  to  be  the  founder  of  a  new  science, 
Galileo  led  a  hard  life.  Though  part  of  a  university, 


THE  PEDIGREE  OF  PHYSICS  121 

he  was  not  a  party  to  its  scholasticism.  So  he  remained 
ever  poor  and  struggling,  was  finally  imprisoned,  and 
died  a  natural  death  only  because  he  deluded  the  officers 
of  the  church.  Yet  to-day  he  alone,  of  all  his  colleagues 
on  the  faculty  at  Padua,  is  remembered  and  honored. 
He  is  the  morning  star  that  heralded  the  new  day  on 
which  the  Germanic  method  of  solving  problems  was 
destined  to  be  applied  to  abstract  thinking. 

Looking  back  a  century  and  a  half  from  Galileo,  we 
see  Guttenberg,  struggling  to  solve  the  problem  of  find- 
ing an  expedient  means  of  satisfying  the  human  need  for 
books.  He,  too,  was  poor  and  oppressed  by  debt,  but 
he  escaped  the  persecution  of  the  Inquisition  because 
his  work  was  "  practical  "  and  did  not  seem  to  endanger 
the  "  absolute  and  infallible  "  ideas  of  Aristotle  and  the 
church.  Yet  was  not  his  work,  too,  fundamental  for 
the  future  of  science,  not  because  he  made  the  diffusion 
of  knowledge  possible,  but  because  he  helped  to  establish 
the  method  of  thinking  that  was  needed  before  science 
could  grow  ? 

41.  Scientific  Industry.  —  Was  the  work  of  Gutten- 
berg the  less  valuable  for  scientific  progress  because  his 
aim  was  the  more  practical?  Is  not  the  method  of 
work  at  least  as  characteristic,  if  not  more  so,  than  is  the 
purpose  or  aim?  Agriculture  is  now  fast  becoming  a 
"  science  "  because  it  is  employing  the  methods  of  science 


122  THE  TEACHING  OF  PHYSICS 

instead  of  following  the  traditions  of  the  past,  although 
its  purpose  still  remains  the  eminently  "  practical " 
one  of  supplying  us  with  food.  All  the  modern  indus- 
tries, in  fact,  are  coming  to  deserve  the  title  of  science, 
although  their  aims  still  remain  unchanged.  It  is,  per- 
haps, needless  to  add  that  the  present  factory  system  of 
manufacture  reduces  the  workmen  to  machines.  Such 
unfortunates  are  engaged  in  neither  industry  nor  science, 
as  here  conceived. 

There  are,  of  course,  differences  in  the  degree  of  refine- 
ment to  which  the  method  is  carried  in  the  cases  of 
industry  and  science,  and  the  purposes  and  aims  of  the 
two  also  differ  in  degree.  But  if  industry  quits  when  an 
"  expedient "  rule  of  thumb  for  the  needs  of  the  imme- 
diate situation  has  been  found,  while  science  continues 
until  the  need  for  a  more  general  rule  or  law  is  discovered, 
is  not  this  a  difference  in  degree  rather  than  one  in  kind  ? 
Bouasse  says :  "  In  the  classification  of  forms,  the  prac- 
tical value  of  a  postulate  is  of  little  importance;  or 
rather  its  value  has  no  significance.  It  is  a  matter  of 
drawing  the  implied  consequences ;  to  reason  well  is  all 
that  is  demanded  of  the  creator  of  a  form." l 

42.  The  Method  of  Science.  —  If  industry  meets 
human  physical  and  mental  needs  by  physical  means 

1  Bouasse,  De  la  Methode  dans  les  Sciences,  p.  102  (Paris,  Alcan, 
1909). 


THE  PEDIGREE  OF  PHYSICS  123 

only,  while  science  forms  theories  and  laws  to  satisfy  the 
intellectual  feelings  of  wonder,  is  not  this  again  a  dif- 
ference of  degree  rather  than  of  kind,  since  both  are 
engaged  in  manipulating  material  things  and  creating 
forms  to  satisfy  human  needs  ?  May  we  not,  then,  define 
the  method  of  science  in  its  broadest  sense,  as  that 
method  which  furnishes  the  most  expedient  solutions 
of  the  problems  defined  by  human  needs?  If  this  con- 
clusion is  accepted,  the  pedigree  of  modern  physics  is 
settled:  Germanic  Industry  is  its  father,  and  Wonder 
is  its  mother.  A  further  definition  of  this  pedigree  will 
be  attempted  in  the  next  chapter. 

SUPPLEMENTARY  READING 

LAMPRECHT,  KARL.  What  is  History?  New  York,  Macmillan, 
1905. 

MANN,  C.  R.  The  History  of  Science  —  An  Interpretation. 
Popular  Science  Monthly,  72,  313  ;  April,  1908. 

CHAMBERLAIN,  HOUSTON  S.  The  Foundations  of  the  Nineteenth 
Century..  Engl.  Tr.  by  John  Lees.  2  vols.  New  York,  Lane, 
1911. 

ADAMS,  G.  B.  Civilization  during  the  Middle  Ages,  Chapters  XI, 
XII.  New  York,  Scribner,  1900. 

FORREST.  Development  of  Western  Civilization,  Chapters  III,  IV. 
University  of  Chicago  Press,  1907. 

LECKY,  W.  E.  H.  The  Rise  and  Influence  of  the  Spirit  of  Rational- 
ism in  Europe.  Vol.  II,  Chapters  V,  VI.  New  York,  Apple- 
ton,  1900. 


124  THE  TEACHING  OF  PHYSICS 

BERGSON,  HENRI.    Creative  Evolution,  Chapter  IV.    New  York, 

Holt,  1910. 
DUHEM,  P.    Essai  sur  la  Notion  de  Theorie  Physique  de  Platan  a 

Galileo.    Paris,  Hermann,  1908. 
MERZ.    History  of  European  Thought  during  the  Nineteenth  Century. 

London,  1903. 
COMTE,  A.    Positive  Philosophy,  Vol.  II,  Chapters  7-11.    London, 

Paul,  1893. 


CHAPTER  VI 
THE  METHOD  OF  PHYSICS 

43.  Method  is  Characteristic.  —  In  the  last  chapter, 
the  fact  that  modern  physics  did  not  begin  to  develop 
until  the  value  of  the  methods  which  it  uses  had  won 
recognition  among  large  bodies  of  men  was  interpreted 
to  mean  that  modern  physics  is  the  child  of  industry. 
This  interpretation  seems  necessary,  if  we  agree  to  classify 
physics  by  its  method  rather  than  by  its  aim  or  purpose. 
Current  ideas  of  modern  science  revolt  at  this  determina- 
tion of  the  pedigree  of  physics,  because  we  at  present 
have,  consciously  or  unconsciously,  come  to  classify  the 
sciences  by  their  aims  rather  than  by  their  methods. 
The  "  pure  "  scientist  is  prone  to  regard  industry  and 
"  applied "  science  after  the  manner  of  the  Greeks ; 
namely,  as  unfit  occupations  for  a  gentleman  and  a 
scholar.  According  to  the  academic  creed,  research  which 
has  no  immediate  practical  application  is  the  "  academic 
ideal "  of  pure  science,  while  the  "  mighty  dollar  "  —  the 
manifest  goal  of  industry  and  applied  science  —  is  but  a 
degraded  "  ideal  of  the  market  place." 

It  is  to  be  hoped,  however,  that  modern  science  will 

125 


126  THE  TEACHING  OF  PHYSICS 

welcome  this  interpretation  of  the  facts  with  the  same 
openmindedness  with  which  it  has  recently  welcomed 
the  ion,  the  electron,  and  the  relativity  postulate.  The 
story  begun  in  the  last  chapter  is  not  yet  finished. 
"  The  child  is  father  of  the  man,"  says  the  old  adage; 
and,  however  paradoxical  this  may  at  first  sight  appear, 
it  contains  a  deep  truth.  In  this  chapter,  the  attempt 
is  made  to  justify  the  classification  of  physics  by  its 
method;  and  in  the  next  we  shall  endeavor  to  show  how 
physics,  the  child  of  industry  in  the  sixteenth  century, 
has  become  father  of  the  man  who,  in  the  twentieth 
century,  has  come  to  be  the  mainstay  and  comfort  of 
his  aged  parent. 

44.  Scientific  Training  not  Transferable.  —  As  has 
been  pointed  out,1  the  more  or  less  conscious  aim  of 
physics  teaching  has  been  to  train  students  to  solve  all 
their  daily  problems  by  the  method  of  science.  That 
this  aim  has  not  yet  been  achieved  is  now  very  generally 
recognized ;  if  for  no  other  reason,  then  simply  because 
men  of  science  themselves,  though  expert  in  the  use  of 
the  method  in  the  field  of  science,  fail  to  use  it  in  solving 
problems  in  economics,  banking,  law,  and  other  "  un- 
scientific "  fields  of  activity.  The  "  mental  discipline  " 
acquired  by  training  in  physics,  while  it  may  lead  to 
skill  in  solving  the  specific  problems  in  physics,  does  not 

1  Ante,  pp.  46  sq. 


[THE  METHOD   OF  PHYSICS  127 

result  in  a  general  ability  to  solve  problems  in  economics 
or  politics  in  a  scientific  manner. 

There  are  two  main  reasons  why  the  training  in  science 
has  not  resulted  in  a  general  ability  to  think  scientifically. 
One  of  these  is  the  vagueness  of  our  ideas  as  to  the  nature 
of  the  method  of  science ;  and  the  other  is  our  ignorance 
until  recently  of  the  conditions  under  which  general 
ability  may  be  developed  by  specific  training.  The 
following  discussion  of  the  methods  of  science  is  intended, 
then,  not  only  to  justify  the  classification  of  physics  by 
its  method,  but  also  to  assist  teachers  in  forming  more 
definite  ideas  concerning  the  nature  of  the  method  of 
science.  The  question  of  the  development  of  general 
ability  by  specific  training  is  reserved  for  Chapter  VIII. 

45.  Definitions  of  the  Method  of  Science.  —  The 
attempts  to  define  the  method  of  science  have  been 
numerous  indeed.  Beginning  with  Bacon's  Novum 
Organum  and  Descartes'  Methode,  and  continuing  on 
down  through  Locke,  Kant,  Whewell,  Mill,  Lotze,  to 
the  recent  works  of  Dewey,  Poincare,  Mach,  Duhem, 
and  others,  we  have  an  unbroken  series  of  profound 
works  whose  study,  while  most  profitable,  is  a  rather 
hopeless  task  for  any  physics  teacher,  loaded,  as  he  is 
sure  to  be,  with  the  endless  details  of  his  daily  routine, 
and  eager  to  keep  pace  with  the  rapid  progress  of  his 
science. 


128  THE  TEACHING  OF  PHYSICS 

Yet,  notwithstanding  the  vast  literature  on  the  sub- 
ject, there  are  numerous  brief  formulae  which  have 
been  worked  out  for  the  guidance  of  teachers  and  which 
are  intended  to  make  it  possible  for  the  teacher  to  teach 
in  such  a  way  that  "  habits  of  scientific  thinking  "  are 
formed  by  students.  One  of  these  brief  statements  has 
already  been  quoted  on  page  47.  For  purposes  of 
discussion  another  such  statement  from  the  preface  of 
a  recent  text  (1902)  is  here  reproduced:  — 

"  This  new  method  of  acquiring  knowledge,  which 
may  be  called  thl.  scientific  method,  has  been  often  dis- 
cussed, and  there  is  substantial  agreement  as  to  the  steps 
which  it  involves.  They  are :  (i)  the  acquisition  of 
individual  facts,  either  by  general  observation  or  by  the 
method  of  artificial  observation  known  as  experimenta- 
tion; (2)  generalization,  the  statement  of  a  general 
relation  which  seems  to  exist  between  these  individual 
facts;  (3)  deduction,  the  making  of  individual  infer- 
ences based  upon  the  generalization  of  the  second  step ; 
and  (4)  experimentation,  to  test  the  accuracy  of  these 
inferences.  A  method  which  starts  in  the  middle  of  the 
process,  by  stating  the  generalization  and  requiring 
the  pupil  to  make  the  deductions  only,  may  give  a 
good  training  in  deductive  reasoning  —  in  algebra  and 
geometry  —  but  it  cannot  teach  physics  nor  give  a 
training  in  the  methods  of  physics.  A  method  which 


THE  METHOD  OF  PHYSICS  129 

makes  the  generalizations  and  deductions  and  calls 
upon  the  pupil  to  verify  these  deductions  by  experiment 
likewise  gives  training  in  but  one  step  of  the  process. 
The  present  textbook  is  a  result  of  the  attempt  of  the 
writer  to  apply  this  scientific  method  in  all  its  steps  to 
the  teaching  of  physics." 

At  first  sight  this  statement  may  seem  to  warrant  the 
"  substantial  agreement  "  which  its  author  claims  for  it. 
But  when  we  turn  to  the  pages  of  the  text,  we  find  the 
subject  introduced  after  this  manner  ^ — 

"  Physics.  —  Physics  is  the  science  which  treats  of 
the  changes  that  take  place  in  the  physical  universe. 

"  The  Physical  Universe.  —  The  physical  universe  is 
that  part  of  the  universe  which  is,  so  far  as  we  know, 
made  up  of  the  two  fundamental  existences,  Matter  and 
Energy. 

"  Matter.  —  No  complete  definition  of  matter  is 
possible.  We  may  learn  of  the  properties  of  material 
bodies,  but  the  essential  nature  of  matter  is  entirely 
unknown  to  us.  The  name  is  generally  understood  to 
mean  the  indestructible  substance  of  all  bodies  which 
are  appreciable  by  our  senses. 

"  Energy.  —  The  essential  nature  of  energy  is  like- 
wise unknown.  We  can  measure  its  quantity,  but  we 
know  nothing  of  its  descriptive  qualities.  It  may  be 
provisionally  defined  as  the  capacity  for  doing  work. 


130  THE  TEACHING  OF  PHYSICS 

"  Work.  —  The  term  work,  as  used  in  physics,  may 
be  defined  as  the  producing  of  such  changes  in  the  rela- 
tive positions  or  relative  motions  of  material  bodies  as 
would  require  an  effort  on  our  part  to  produce." 

The  subject  of  wave  motion  and  sound  is  thus  intro- 
duced in  this  same  book :  — 

"  Scope  of  the  Subject.  —  The  form  of  energy  trans- 
ference known  as  wave  motion  is  best  studied  in  its 
relations  to  the  phenomena  of  sound  and  light.  Sound 
and  light  differ  from  other  branches  of  Physics  in  that 
they  involve  both  a  physical  and  a  physiological  side. 
The  physical  side  of  the  subject  of  sound  is  principally 
concerned  with  wave  motions  in  elastic  bodies.  The 
physiological  side  is  concerned  with  the  sensations  pro- 
duced in  the  hearing  organ  by  means  of  these  wave 
motions. 

"  First  Law  of  Sound.  —  The  fundamental  proposi- 
tion in  the  study  of  sound  is  that  all  sounding  bodies 
are  in  a  state  of  vibration.  These  vibrations  may  be 
observed  in  a  number  of  characteristic  sounding  bodies 
by  means  of  the  following  experiments." 

Many  other  passages  of  like  character  are  found  in 
the  book,  showing  an  utter  failure  on  the  part  of  the 
author  to  follow  the  formula  of  method  which  he  himself 
has  set  up.  And  if  he  could  not  follow  it  himself,  how 
can  we  expect  others  to  do  so  ?  Hence,  the  first  conclu- 


THE  METHOD  OF  PHYSICS  131 

sion  to  be  drawn  concerning  this  formula,  which  claims 
to  be  descriptive  of  the  scientific  method,  is  that  it  is 
fairly  useless  to  the  teacher. 

46.  The  Real  Method.  —  The  reason  for  its  useless- 
ness  is  not  hard  to  find  if  we  attempt  to  apply  it  to  a 
concrete  case.  Did  Galileo  follow  it  when  he  proved  that 
bodies  of  different  masses  fall  with  the  same  accelera- 
tion? Many  will  answer  this  question  in  the  affirma- 
tive, since  Galileo  certainly  did,  on  the  basis'  of  his 
general  observations  on  falling  bodies,  form  the  hy- 
pothesis that  they  fall  with  the  same  acceleration,  and 
then  proceed  to  verify  the  hypothesis.  In  this  formal 
sense,  he  may  be  said  to  have  followed  the  formula. 

But  what  was  it  that  led  Galileo  to  undertake  the 
investigation?  Thousands  upon  thousands  of  others 
had  observed  falling  bodies  as  well  as  Galileo.  Why  was 
it  reserved  for  him  to  make  the  discovery?  Was  it 
not  because  he  had  read  or  heard  of  Aristotle's  dogmas 
on  this  subject  and  had  been  led  to  wonder  whether  they 
could  really  be  in  accord  with  the  facts?  Thus  scientific 
thinking  does  not  begin  with  a  mere  collection  of  facts ; 
it  starts  when  some  man  begins  to  wonder  what  the  facts 
really  are  and  what  they  really  mean;  i.e.  when  some 
discrepancy  is  felt  between  the  observed  facts  and  their 
accepted  interpretation. 

And  is  not  this  ability  to  sense  discrepancies  in  a  situa- 


132  THE  TEACHING  OF  PHYSICS 

tion  —  to  feel  that  there  is  somehow  a  gap  that  needs 
bridging  or  a  contradiction  that  needs  adjustment  — 
one  of  the  chief  factors  that  distinguishes  the  man  of 
genius  from  other  mortals  ?  If  Galileo  had  been  unable 
to  sense  the  discrepancy  and  to  formulate  the  problem, 
he  would  never  have  attempted  its  solution.  In  like 
manner,  unless  Newton  had  felt  that  there  was  some- 
thing wanting  in  his  knowledge  about  gravity,  —  did 
its  action  extend  to  the  moon  or  not  ?  —  he  could  never 
have  solved  the  problem  and  established  his  theory  of 
universal  gravitation.  Surely,  then,  this  sensing  of 
gaps,  this  feeling  of  discrepancies,  is  a  fundamental  part 
of  scientific  thinking.  No  scientist  ever  goes  about 
gathering  data  unless  he  thinks  they  will  be  useful  to 
him  in  accomplishing  something  he  really  wants  to  do. 
It  is  this  desire,  this  longing  to  find  out  on  his  part, 
that  furnishes  the  motive  that  keeps  him  at  work.  Yet 
the  steps  in  the  scientific  method  as  just  outlined  make 
no  mention  of  this  spring  of  motive  from  which  all  think- 
ing flows.  And  is  it  reasonable  to  imagine  that  children 
will  become  scientific  thinkers  if  we  simply  put  them 
through  the  motions  called  for  by  the  steps  in  the  formula, 
unless  we  also  induce  in  them  motives  in  some  way  similar 
to  those  which  impel  real  scientists  doing  real  investiga- 
tion ?  When  Galileo  first  beheld  the  satellites  of  Jupiter 
through  his  telescope,  he  is  said  to  have  fallen  on  his 


THE  METHOD  OF  PHYSICS  133 

knees  and  fervently  thanked  God  for  having  revealed 
to  him  such  unsuspected  wonders.  And  was  not  Archi- 
medes so  overcome  with  enthusiasm  over  the  discovery 
of  his  principle  that  he  completely  forgot  the  proprieties 
of  the  occasion  and  ran  about  in  charming  dishabille, 
shouting  "  Eureka !  "  Is  there  any  teacher  to-day  any- 
where who  ever  observed  any  boy  or  girl  become  enthused 
with  any  such  emotions  as  these  after  performing  any 
one  of  the  "  forty  experiments  from  the  following  list  "  ? 
"  If  any,  speak ;  for  him  have  I  offended !  " 

47.  Logic  Follows  Intuition.  —  This,  then,  is  the  first 
reason  why  the  formula  given  above  for  scientific  think- 
ing is  useless.  It  fails  to  take  account  of  the  emotional 
element.  Therefore,  it  cannot  direct  teachers  in  the 
paths  of  imparting  knowledge,  since  "  knowledge  is 
impossible  without  feeling  and  will."1  Because  it  thus 
fails  to  recognize  the  functions  of  the  emotions,  it  is 
but  a  form  of  Platonic  thought.  It  describes  the  logical 
steps  which  a  mature  mind  can  see  might  have  been  used 
in  obtaining  the  result  after  the  result  has  been  obtained 
by  more  unconscious  and  tentative  methods.  No  one 
ever  follows  such  a  cut-and-dried  form  of  thinking  when 
he  is  solving  a  real  problem.  A  physician  trying  to 
diagnose  a  case  is  constantly  making  hypotheses,  deduc- 
tions, and  verifications ;  he  is  selecting,  dissociating,  and 
1  Dewey,  Psychology,  p.  18  (New  York,  Harper,  1897). 


134  THE  TEACHING  OF  PHYSICS 

associating  ideas  even  while  he  is  asking  questions  about 
symptoms,  taking  the  pulse,  watching  the  respiration, 
and  so  on.  After  he  has  solved  the  problem,  he  may 
organize  it  in  his  mind  under  the  heads  of  the  formula 
given,  but  this  is  only  after  he  has  reached  the  conclusion 
by  less  formal  methods. 

Such  formulae  for  the  method  of  science  have  their 
place  in  treatises  on  logic,  where  the  effort  is  made  to 
devise  a  "  form  "  into  which  thinking  processes  may  be 
made  to  fit.  But  in  actual  life  thinking  is  too  subtle 
and  flighty  an  operation  to  permit  its  reduction  to  any 
such  simple  forms.  They  are  the  useful  tools  and  cate- 
gories of  the  logician,  rather  than  safe  rules  for  a  teacher 
to  follow.  We  should  never  forget  that  "  Demonstra- 
tions are  constructed  by  logic,  but  inventions  are  made 
through  intuition.  To  know  how  to  criticise  is  good; 
but  to  know  how  to  create  is  better.  Logic  teaches 
us  that  on  such  or  such  a  path  we  are  sure  to  meet  no 
obstacles ;  but  it  does  not  tell  us  which  path  it  is  that 
leads  to  the  goal.  In  older  to  find  this  out,  we  must 
see  the  goal  from  a  distance,  and  the  ability  that  enables 
us  to  do  this  is  intuition.  Without  this,  the  geometer 
would  be  like  a  writer  whose  attention  was  riveted  on 
the  grammar,  but  who  had  no  ideas."1 

"  The  philosophy  that  investigates  nature  is  philoso- 
1  Poincar6,  Science  et  Methode,  p.  137  (Paris,  Alcan,  1909). 


THE  METHOD   OF  PHYSICS  135 

phy  as  science;  for  this  reason  it  is  distinct  from  that 
dangerous  and  ever  fruitless  thing :  philosophy  as  logic. 
...  To  appeal  to  pure  logic  for  an  interpretation  of  the 
world,  —  to  logic  and  not  to  intuition,  —  and  to  fail  to 
raise  experience  to  the  position  of  giver  of  laws,  simply 
means  willfully  to  bind  truth  in  chains.  .  .  .  Hence,  the 
new  period  of  philosophy  investigating  nature  began  with 
a  general  insurrection  against  Aristotle.  For  this  Greek 
not  only  analyzed  the  formal  laws  of  thought,  thus 
rendering  their  use  more  certain,  and  for  which  he 
deserves  the  gratitude  of  all  future  races,  but  he  also 
undertook  to  solve  by  means  of  logic  all  problems  that 
were  not  yet  investigated,  and  even  those  that  were  not 
amenable  to  investigation.  On  this  account  science 
was  impossible ;  for  the  silent  assumption  of  logic  is  that 
man  is  the  measure  of  all  things,  when  in  reality  —  as  a 
purely  logical  being  —  he  is  not  even  a  measure  of  him- 
self. ...  In  the  entire  system  of  Aristotle,  logic,  instead 
of  being  the  servant,  sits  as  queen  upon  the  throne."  1 

It  is,  of  course,  essential  that  the  teacher  of  science 
should  know  logic,  but  he  must  be  wary  of  applying  his 
mature  logic  too  abruptly  in  his  teaching.  Intuition  is 
the  forerunner  of  logic  in  the  method  of  science;  and 
"  the  conscious  setting  forth  of  the  method  logically 
adapted  for  reaching  an  end  is  possible  only  after  the 

1  Chamberlain,  Die  Grundlagen  des  Neunzehnten  Jahrhundcrts,  p.  899. 


136  THE  TEACHING  OF  PHYSICS 

result  has  been  reached  by  more  unconscious  and  tenta- 
tive methods.  Ability  to  divide  a  subject,  to  define  its 
elements,  and  to  group  them  into  classes  according  to 
general  principles,  represents  logical  capacity  at  its  best, 
reached  after  thorough  training.  But  it  is  absurd  to 
suppose  that  a  mind,  which  needs  such  training  because 
it  cannot  perform  these  operations,  can  begin  where  the 
expert  mind  stops.  The  logical  from  the  standpoint  of 
subject  matter  represents  the  goal,  the  last  term  of  training, 
not  the  point  of  departure.  In  truth,  the  mind  at  every 
stage  of  development  has  its  own  logic."  1 

The  elements  of  the  method  of  physics  to  which  we  have 
thus  far  endeavored  to  draw  attention  are,  then :  i .  The 
emotion  of  wonder  which  comes  first,  senses  the  problem, 
and  is,  therefore,  the  "  originator  and  continuer  of 
science  " ;  2.  The  importance  of  intuition  in  "  seeing 
the  goal  from  afar  " ;  and  3.  The  position  of  logic  as 
servant  rather  than  queen,  —  as  a  bodyguard  that 
follows  after  and  helps  intuition  in  removing  obstacles 
on  the  way  to  the  goal.  These  factors  are  here  empha- 
sized because,  although  they  are  the  fundamentally 
important  ones  for  teachers,  they  seem  to  have  escaped 
general  notice  in  the  numerous  and  vast  literature  of 
this  subject.  This  is  one  of  the  results  of  Platonic 
thought. 

1  Dewey,  How  We  Think,  pp.  113,  62. 


THE  METHOD  OF  PHYSICS  137 

48.  The  Concrete  and  the  Abstract.  —  Besides  these 
three  factors,  there  are  several  others  which,  if  not 
grasped  by  the  teacher,  will  impair  his  success  in  training 
in  scientific  thinking.  The  first  of  these  is  the  relation 
between  the  concrete  and  the  abstract.  As  has  been 
already  pointed  out,  "  the  origin  of  thinking  is  some 
perplexity,  confusion,  or  doubt.  Thinking  is  not  a  case 
of  spontaneous  combustion;  it  does  not  occur  just  on 
'  general  principles,'  There  is  something  specific  which 
occasions  and  evokes  it.  General  appeals  to  a  child 
(or  to  a  grown-up)  to  think,  irrespective  of  the  existence 
in  his  own  experience  of  some  difficulty  that  troubles  him 
and  disturbs  his  equilibrium,  is  as  futile  as  advice  to  lift 
himself  by  his  boot  straps." 1 

"  Thinking  must  end  as  well  as  begin  in  the  domain  of 
concrete  observations,  if  it  is  to  be  complete  thinking."  2 
The  usefulness  of  this  sentence  depends  on  the  meaning 
attached  to  the  word  "  concrete."  Most  people  seem  to 
think  that  anything  which  is  "  made  of  matter  "  —  a 
sidewalk,  a  house,  a  mathematical  model,  or  a  piece  of 
physical  apparatus  —  is  concrete  to  everybody  because 
it  is  a  material  thing.  According  to  this  classification, 
the  concrete  is  marked  off  from  the  abstract  by  a  fixed 
boundary  which  is  the  same  for  everybody,  namely,  that 
between  matter  and  non-matter.  According  to  this 

1Dewey,  Ibid.,  p.  12.  2  Ibid.,  p.  96. 


138  THE  TEACHING  OF  PHYSICS 

conception,  it  is  immaterial  what  material  thing  is  used 
to  introduce  a  topic  in  physics ;  an  unfamiliar  piece  of 
what  Poincare  calls  "  bizarre  apparatus  "  will  do  just  as 
well  as  some  familiar  thing  from  the  child's  own  expe- 
riences; since  both  are  made  of  matter  and  hence 
"  concrete." 

Yet  the  concrete  cannot  be  so  definitely  marked  off 
from  the  abstract.  "  To  one  who  is  thoroughly  at  home 
in  physics  and  chemistry,  the  notions  of  atom  and  molecule 
are  fairly  concrete.  They  are  constantly  used  without 
involving  any  labor  of  thought  in  apprehending  what 
they  mean.  The  terms  convey  meaning  so  directly  that 
no  effort  at  translating  is  needed.  Concrete  denotes  a 
meaning  definitely  marked  off  from  other  meanings,  so 
that  it  is  readily  apprehended  by  itself.  Thus  the  con- 
crete is  purely  relative  to  the  intellectual  progress  of  an 
individual ;  what  is  abstract  at  one  period  of  growth  is 
concrete  at  another.  There  is,  nevertheless,  a  general 
line  of  cleavage  which,  deciding  upon  the  whole  what 
things  fall  within  the  limits  of  familiar  acquaintance  and 
what  without,  marks  off  the  concrete  from  the  abstract 
in  a  more  permanent  way.  These  limits  are  fixed  mainly 
by  the  demands  of  practical  life.  Things  such  as  sticks 
and  stones,  meat  and  potatoes,  houses  and  trees,  are 
such  constant  features  of  the  environment  of  which  we 
have  to  take  account  in  order  to  live,  that  their  impor- 


THE  METHOD  OF  JPHYSICS  139 

tant  meanings  are  soon  learned,  and  indissolubly  associ- 
ated with  objects." 

"By  contrast,  the  abstract  is  the  theoretical,  or  that 
not  intimately  associated  with  practical  concerns.  The 
abstract  thinker  deliberately  abstracts  from  application 
in  life ;  that  is,  he  leaves  practical  uses  out  of  account. 
What  remains  when  connections  with  use  and  applica- 
tion are  excluded  ?  Evidently  only  what  has  to  do  with 
knowing  considered  as  an  end  in  itself.  Many  notions 
of  science  are  abstract,  not  only  because  they  cannot  be 
understood  without  a  long  apprenticeship  in  the  science, 
but  also  because  the  whole  content  of  their  meaning  has 
been  framed  for  the  sole  purpose  of  facilitating  further 
knowledge,  inquiry,  and  speculation.  When  thinking  is 
used  as  a  means  to  some  end,  good,  or  value  beyond  it- 
self, it  is  concrete ;  when  it  is  employed  simply  as  a  means 
to  more  thinking,  it  is  abstract."  1 

The  foregoing  definitions  of  the  concrete  and  the  ab- 
stract are  not  only  the  clearest,  but  also  the  most  useful 
ones  available  for  the  teacher.  According  to  them,  a 
piece  of  physical  apparatus,  like  that  used  to  introduce 
the  subject  of  Pascal's  law  on  page  86,  is  not  concrete 
to  the  pupils  simply  because  it  "  occupies  space  and 
affects  the  senses,"  i.e.  because  it  is  made  of  matter. 
On  the  other  hand,  the  water  taps  in  the  school  or  the 

1  Dewey,  How  We  Think,  pp.  136-138. 


140  THE  TEACHING  OF  PHYSICS 

home,  together  with  the  fact  that  the  water  rushes  out 
more  violently  in  the  cellar  than  on  the  third  floor,  are 
concrete  to  the  pupils  because  familiar  and  filled  with 
significance  for  their  daily  lives.  Such  concrete  material 
furnishes  a  suitable  starting  point  for  the  discussion  of 
Pascal's  law,  and  supplies  a  ready  basis  for  the  definition 
of  a  problem.  When  a  state  of  uncertainty  as  to  what  the 
water  will  do,  or  as  to  how  the  piping  is  arranged  to 
produce  the  observed  effects  has  been  induced,  thinking 
begins.  It  is  then  easy  to  lead  on  to  an  hypothesis  and 
thence  to  experiments  and  measurements. 

49.  Wide  Association  Necessary.  —  There  is  another 
fundamental  reason  why  it  is  important  to  introduce 
topics  with  the  concrete  as  just  defined.  The  water 
system  is  already  associated  in  the  pupil's  mind  with  a 
wide  range  of  experiences.  When  he  has  achieved  the 
law  on  the  basis  of  such  concrete  material,  he  finds  no 
difficulty  in  applying  the  law  to  practical  cases.  The 
law  becomes  associated  automatically  with  the  experi- 
ences because  of  its  mode  of  development  in  his  mind. 
Every  physics  teacher  wonders  why  pupils  find  it  so 
difficult  to  apply  the  principles  of  physics  to  daily  life. 
The  difficulty  is  due  in  large  measure  to  the  failure  to 
begin  the  discussions  with  material  that  is  concrete  to  the 
pupil.  By  beginning  with  apparatus  or  principles  that 
are  really  abstract  to  him,  we  fail  to  make  use  of  the  wide 


THE   METHOD   OF  PHYSICS  141 

range  of  associations  always  grouped  about  a  truly  con- 
crete idea ;  and  if  the  discussion  is  thus  abstract  at  the 
beginning,  no  amount  of  exhortation  on  the  part  of  the 
teacher  will  make  it  possible  for  the  pupil  to  bring  it 
back  to  earth  again. 

50.  The  Place  of  Applications.  —  One  other  point  on 
this  topic  needs  to  be  noted.  "  Thinking  must  end  as 
well  as  begin  in  the  domain  of  concrete  observations,  if 
it  is  to  be  complete  thinking."  *  All  textbooks  have 
problems  and  exercises  after  the  demonstration  of  a  prin- 
ciple, thus  recognizing  the  need  of  ending  in  the  "  domain 
of  concrete  observations."  But  if  these  problems  are  of 
the  type  quoted  on  page  89,  they  are  not  concrete  as  here 
denned.  They  are  not  taken  from  real  experience,  and 
the  ideas  which  they  contain  —  dyne,  energy,  accelera- 
tion, tth  second,  etc.  —  are  to  the  pupils  abstract.  Such 
problems  are  merely  problems  that  are  made  up  to  be 
problems  and  do  not  present  concrete  situations  in  which 
there  is  some  discrepancy  to  be  cleared  up  or  some  gap 
to  be  filled. 

Many  books  refer  to  machines  and  daily  experiences 
at  the  end  of  the."  demonstration  "  of  a  principle,  citing 
them  as  "  applications."  This  practice  is  good,  provided 
the  demonstration  also  began  with  familiar  concrete 
material.  "  The  true  purpose  of  exercises  that  apply 

1  Dewey,  How  We  Think,  p.  96. 


142  THE  TEACHING  OF  PHYSICS 

rules  and  principles  is  not  so  much  to  drive  or  drill  them 
in  as  to  give  adequate  insight  into  an  idea  or  principle. 
To  treat  application  as  a  separate  final  step  is  disastrous. 
.  .  .  When  the  general  meaning  is  regarded  as  complete  in 
itself,  application  is  treated  as  an  external,  non-intellec- 
tual use  to  which,  for  practical  purposes  alone,  it  is  ad- 
visable to  put  the  meaning.  The  principle  is  one  self- 
contained  thing;  the  use  is  another  and  independent 
thing.  When  this  divorce  occurs,  principles  become  fos- 
silized and  rigid ;  they  lose  their  inherent  vitality,  their 
self-impelling  power.  .  .  .  The  teacher  needs,  indeed, 
to  supply  conditions  favorable  to  use  and  exercise ;  but 
something  is  wrong  when  artificial  tasks  have  arbitrarily 
to  be  invented  in  order  to  secure  application  for  prin- 
ciples." l 

51.  The  Method  of  Physics. — While  a  physicist  is 
laboring  over  a  real  scientific  research  in  physics,  he  finds 
it  difficult,  if  not  impossible,  to  guide  his  thinking  accord- 
ing to  any  logical  formula.  But  when  he  has  solved  his 
problem,  he  describes  the  process  by  telling  how  he  first 
sensed  an  inconsistency,  or  a  discrepancy,  or  a  gap  in  a 
system  of  ideas  which  were  concrete  to  him ;  how  he  then, 
by  search  for  related  ideas  and  facts,  or  by  both,  suc- 
ceeded in  defining  the  problem  sharply  ;  how  he  formed 
a  plan  of  action  or  theory  to  serve  as  a  tentative  solution 
1  Dewey,  How  We  Think,  p.  212. 


THE  METHOD   OF  PHYSICS  143 

of  the  problem ;  and,  finally,  how  he  deduced  the  con- 
sequences of  the  theory  and  tested  them  by  experiment. 
This  is  excellent  logical  form  for  telling  about  his  in- 
vestigation after  it  is  done.  But  it  is  clear  enough  that 
he  never  laid  out  his  investigation  in  advance  in  any  such 
sharply  defined  steps.  During  the  process  of  the  solu- 
tion of  the  problem,  he  was  constantly  associating,  dis- 
sociating, and  ordering  ideas,  making  inductions,  deduc- 
tions, and  verifications ;  and,  in  short,  thinking  as  we  all 
think  by  processes  that  are  too  complex  to  be  analyzed. 
So  it  is  with  the  children.  We  cannot  teach  them  to 
think;  they  already  do  this.  We  can,  however,  help 
them  to  learn  to  think  well.  But  this  result  is  not  likely 
to  follow  a  series  of  mental  gymnastics  which  are  ordered 
according  to  a  logical  formula  that  was  constructed  on 
the  basis  of  post  mortem  examinations  of  scientific  work. 
The  teacher  is  much  more  likely  to  succeed  if  he  creates 
such  a  situation  that  the  pupils  will  sense  inconsistencies 
and  begin  to  wonder  what  the  trouble  is.  He  may  then 
criticise  their  attempts  at  defining  the  problem,  may 
follow  out  with  them  the  consequences  of  their  guesses  at 
its  solution,  and  encourage  them  to  seek  in  the  laboratory 
the  further  information  that  may  be  needed,  and  that 
cannot  be  obtained  except  in  the  laboratory.  In  short, 
the  teacher  will  be  more  likely  to  succeed  in  training  the 
pupils  in  good  thinking  if  he  becomes  like  the  kodak 


144  THE  TEACHING  OF  PHYSICS 

fiend  —  "he  presses  the  button  and  the  children  do  the 
rest." 

52.  The  Truth  of  Physical  Laws.  —  One  final  point 
which  is  of  the  greatest  importance  to  teachers  remains 
to  be  noted.  It  is  the  question  of  the  truth  of  the  laws 
of  physics.  At  present  many  pupils  leave  the  physics 
classes  with  the  impression  that  the  physicists  have 
settled  every  possible  problem  in  physics  because  they 
have  discovered  "  laws,"  which  "  govern  "  nature  and 
are  eternally  fixed  and  immutable,  —  veritable  Platonic 
ideas. 

Nothing  can  be  less  true  than  this.  For  in  the  first 
place,  laws  express  relations  between  variable  quantities, 
and  the  "  form  "  of  these  relations  is  determined  by  fitting 
measurements  to  a  theory.  But  all  measurements  are 
approximate,  and  never  exact.  Therefore,  they  never 
do  fit  exactly,  or  absolutely  into  the  "  form."  More 
exact  measurements  sometimes  bring  observations  more 
closely  into  accord,  so  that  they  more  nearly  satisfy 
the  law  or  form  selected;  and  sometimes  they  lead 
to  the  discovery  of  new  factors  and  make  necessary 
a  change  in  the  law.  But  in  any  case,  they  are 
never  absolutely  correct,  and  so  the  laws  remain  true  to 
their  Germanic  characteristic  of  approximation.  Every 
teacher  admits  this  freely,  but  many  fail  to  impress  it 
on  the  pupils. 


THE  METHOD  OF  PHYSICS  145 

On  close  examination,  the  laws  of  physics  are  found 
to  be  even  less  immutable  than  is  implied  in  the  fact 
that  they  are  close  approximations.  They  are  but  human 
interpretations  of  natural  phenomena,  and  there  is  noth- 
ing to  prevent  new  interpretations  from  being  made  at 
any  time,  provided  only  that  they  square  with  all  the 
known  facts.  Such  new  interpretations  are  constantly 
being  made  and  are  one  of  the  sources  of  continual  growth. 
In  some  cases,  as,  for  example,  when  the  phenomena  of 
light  were  interpreted  in  terms  of  electricity,  we  are  able 
to  check  up  the  new  interpretation  and  prove  it  to  be  an 
improvement  on  the  old  one,  in  that  it  resumes  more 
phenomena  under  fewer  ideas. 

But  in  other  cases,  as  in  the  non-Euclidean  geometry 
and  the  relativity  postulate,  we  have  not  yet  been  able  to 
prove  by  experiment  that  these  interpretations  are  truer 
or  more  exact  than  those  now  in  use.  In  such  cases,  we 
choose  not  on  the  basis  of  truth,  but  on  the  basis  of  con- 
venience. As  Poincare  puts  it  in  regard  to  the  adoption 
of  the  Euclidean  geometry : 1  "  Our  mind  has  adopted 
the  geometry  most  advantageous  to  the  species,  or,  in 
other  words,  most  convenient.  Geometry  is  not  true, 
it  is  advantageous."  Again : 2  "  This  affirmation :  '  the 
earth  turns  round  '  has  no  meaning,  since  it  can  be  veri- 
fied by  no  experiment ;  since  such  an  experiment  not  only 
1  Poincar6,  Science  and  Hypothesis,  p.  65.  z  Ibid.,  p.  85. 


146  THE  TEACHING  OF  PHYSICS 

could  not  be  either  realized  or  dreamed  by  the  boldest 
Jules  Verne,  but  cannot  be  conceived  of  without  contra- 
diction ;  or  rather  these  two  propositions :  '  the  earth 
turns  round '  and  '  it  is  more  convenient  to  suppose  the 
earth  turns  round '  have  the  same  meaning ;  there  is 
nothing  more  in  one  than  in  the  other." 

It  is  difficult  for  us,  who  have  come  to  accept  the  state- 
ment '  the  earth  turns  round  '  as  absolutely  true,  to  real- 
ize that  this  is  but  the  most  convenient  and  simplest 
interpretation  yet  found  of  all  the  facts  of  experience. 
The  evidence  in  favor  of  this  interpretation  is  so  over- 
whelming, that  we  feel  a  distinct  repugnance  against 
admitting  it  to  be  only  "  expedient."  This  feeling  of 
repugnance  is  even  more  marked  when  it  is  suggested 
that  Euclidean  geometry  is  not  a  body  of  necessary  truth 
imposed  on  us  from  on  high,  but  only  the  simplest  and 
most  convenient  method  of  interpretation  of  space  re- 
lations. Yet  no  one  should  refuse  to  accept  this  latter 
conclusion  until  he  has  studied  carefully  Poincare's 
essays  1  on  the  subject.  His  conclusion  is  particularly 
cogent  when  he  says :  "  Why  be  astonished,  then,  at 
the  resistance  which  we  make  to  any  attempt  to  disso- 
ciate things  that  have  long  been  associated?  It  is  this 
resistance  itself  which  we  call  the  evidence  of  geometrical 

1  Especially  Part  II  on  Space  in  Science  and  Hypothesis,  and  Book  II, 
Chapter  I,  on  the  Relativity  of  Space  in  Science  et  Methode. 


THE  METHOD  OF  PHYSICS  147 

truth ;  this  evidence  is  nothing  else  than  the  repugnance 
which  we  feel  in  breaking  up  very  old  habits  with  which 
we  have  always  been  satisfied."  1 

If  we  accept  the  conclusion  that  the  laws  of  science  are 
true  only  in  so  far  as  they  are  found  to  be  the  most  ad- 
vantageous interpretations  of  phenomena,  the  difference 
between  the  speculations  of  Plato  and  Aristotle  and  the 
laws  of  modern  physics  becomes  very  striking.  The 
"  ideas  "  of  the  former  were  immutable,  absolute,  and 
imposed  on  men  from  on  high ;  their  doctrines  were 
dogmatic,  and  thinking  was  a  discreet  function  of  the 
human  mind  and  the  only  one  that  could  lead  to  "  one- 
ness with  the  absolute."  By  contrast,  the  interpreta- 
tions of  modern  physics  are  tentative,  relative,  and 
wrought  by  human  industry ;  its  laws  have  been  found 
to  be  expedient  guides  in  forecasting  the  future,  and 
thinking  is  only  one  of  several  coordinate  factors  in  the 
activities  of  a  living,  feeling  humanity. 

Greek  thought  has  been  useful  to  modern  physics  in 
furnishing  many  ideas  that  were  the  inconsistent  elements 
in  situations  in  which  problems  became  defined,  as  in  the 
case  of  Galileo  mentioned  on  page  131.  The  absolute, 
the  immutable,  the  pure  thinker,  the  proud  know-it-all, 
are  Greek ;  the  relative,  the  ever  changing,  the  indus- 
trious doer,  the  humble  seeker  for  larger  truth,  are  Ger- 
1  Science  et  Methode,  p.  108. 


148  THE  TEACHING  OF  PHYSICS 

manic.     Well  may  modern   physics   say  with 
"  Timeo  Danaos,  dona  ferentes." 

SUPPLEMENTARY  READING 

DEWEY,  JOHN.    How  We  Think.    Boston,  Heath,  1910. 

Studies  in  Logical   Theory,  Chapters   1-4.     University  of 

Chicago  Press,  1903. 

POINCARE,  H.    Science  and  Hypothesis,  Chapters  V,  IX.     New 
York,  The  Science  Press,  1905. 

The  Value  of  Science,  Chapters  I,  V,  VII,  X,  XI.    New 
York,  The  Science  Press,  1907. 

Science  et  M&thode,  Book  I,  Chapter  I ;  Book  II,  Chapters 

I-III.     Paris,  Flammaron,  1909. 

NUNN,  T.  P.  The  Aims  and  Achievements  of  the  Scientific  Method. 
New  York,  Macmillan,  1907. 

Section  VI,  in  Adamson,  Practice  of  Instruction.    London, 

National  Society  Depository,  1907. 

STRONG.  Lectures  on  the  Method  of  Science,  Chapters  I-II.  Ox- 
ford, Clarendon  Press,  1906. 

HODSON,  F.  Broad  Lines  in  Science  Teaching,  Introduction  and 
Chapters  I,  VI,  VII,  IX,  XVIII-XXI.  London,  Macmillan, 
1910. 

MIVART.  Groundwork  of  Science.  Chapters  3-5.  New  York,  Put- 
nam, 1908. 

DUHEM,  P.  La  Theorie  Physique,  son  Objet  et  sa  Structure.  Paris, 
Chevalier  et  Reviere,  1906. 

VOLKMANN,  P.  Erkentnisstheoretische  Grundzuge  der  Naturwissen- 
schaft.  2d  ed.  Leipzig,  Teubner,  1910. 

HARTMANN,  EDW.  VON.  Die  Weltanschauung  der  Modernen  Physik, 
Bad  Sachse,  Haake,  1909. 

BOUASSE,  H.  De  la  Meihode  dans  Us  Sciences,  pp.  73-110.  Paris, 
Alcan,  1009. 


CHAPTER  VII 

THE  BIOGRAPHY  OF  PHYSICS 

53.  What  are  the  Characteristics  of  Physics?  —  In 
Chapter  V  the  hypothesis  was  advanced  that  modern 
physics  is  the  child  of  industry,  and  the  justification  for 
this  hypothesis  was  found  in  the  fact  that  the  positive 
method  of  thinking,  which  is  the  stronghold  of  physics, 
had  to  win  recognition  among  large  masses  of  men,  by 
proving  that  it  was  the  only  method  capable  of  giving 
expedient  solutions  of  industrial  and  commercial  prob- 
lems, before  physics  could  begin.  Having  proved  its 
worth  in  solving  these  concrete  problems,  the  time  was 
ripe  for  its  application  to  more  abstract  problems. 

It  was  also  pointed  out  that  the  motives  that  lead  men 
to  study  these  more  abstract  problems  are  very  different 
from  those  which  impel  men  in  industry  and  commerce ; 
still  it  seemed  more  advantageous  to  classify  physics 
with  Germanic  industry,  thus  regarding  their  common 
method  as  the  more  important  factor,  than  to  continue 
to  think  of  its  motive  as  all  important  and  to  classify  it 
with  Platonic  thought.  As  has  been  statedr  this  classi- 
fication will  seem  to  many  to  be  degrading  to  physics. 

149 


150  THE  TEACHING  OF  PHYSICS 

Those  who  feel  this  way  about  it  should  remember  that 
several  of  the  sons  of  industry  have  made  the  best  Presi- 
dents this  country  has  ever  had ;  and  there  is  no  sufficient 
reason  why  the  child  of  wonder  and  industry  should  not 
have  possessed  other  traits  of  character  that  were  as  im- 
portant in  making  him  great  as  was  the  method  and  the 
spirit  inherited  from  his  parents.  We  shall  seek  to  dis- 
cover such  traits  in  the  following  study  of  the  develop- 
ment of  the  child. 

54.  Galileo's  Work.  —  Galileo  is  justly  regarded  as 
the  founder  of  modern  physics.  He  is  usually  mentioned 
in  the  elementary  texcbooks  because  of  his  experiment 
on  the  Tower  of  Pisa  and  his  discovery  of  the  relation 
between  distance  and  time  for  freely  falling  bodies. 
In  some  of  the  more  advanced  texts,  the  modern  ideas 
of  force  and  inertia  are  ascribed  to  him,  while  others  give 
credit  for  these  to  Newton.  Now  if  these  are  the  sole 
claims  of  Galileo  to  honor,  the  children  of  to-day  are 
little  interested  in  him  or  his  work.  When  the  teacher 
has  carefully  repeated  the  experiment  of  rolling  the  balls 
down  the  inclined  plane,  and  has  demonstrated  that  the 
distances  are  proportional  to  the  squares  of  the  time 
intervals,  are  not  the  children  almost  sure  to  react  with 
a  feeling  of  "  Well,  what  of  it?  "  Why  should  they  care 
whether  the  distances  are  proportional  to  the  squares  or 
to  the  cubes  of  the  time  intervals?  What  can  they  do 


THE  BIOGRAPHY  OF  PHYSICS  151 

with  the  information?  Does  it  solve  any  problem  of 
their  own  making  or  remove  inconsistencies  in  some  real 
situation  that  is  concrete  to  them?  Is  there  nothing 
more  than  these  meager  facts  to  be  secured  from  a  study 
of  Galileo's  work? 

The  reply  of  the  current  academic  physics  is :  "  Yes, 
from  his  experiments  with  the  inclined  plane,  he  showed 
what  acceleration  is,  developed  the  scientific  idea  of 
inertia,  and  gave  us  the  modern  notion  of  force  as  the 
cause  of  acceleration."  Very  well,  but,  though  the  physi- 
cist may  know  how  to  appreciate  the  value  of  this  infor- 
mation, will  the  great  majority  of  the  pupils  cease  to  ask : 
"  Well,  what  of  it?  What  more  can  we  do  with  these 
ideas  than  with  the  commonplace  ideas  of  inertia,  veloc- 
ity, and  force  ?  " 

It  seems  strange  that  the  schoolbooks  are  satisfied  to 
present  only  this  much  of  Galileo's  work,  and  to  assume 
tacitly  one  other  important  point  which  Galileo  thought 
it  necessary  to  consider  theoretically  and  to  prove  ex- 
perimentally. As  is  well  known,  he  tried  the  experiment 
of  rolling  balls  down  the  inclined  plane  because  the  freely 
falling  ball  moved  too  quickly  to  be  observed  with  ac- 
curacy by  the  means  at  his  disposal.  So  after  he  had 
determined  the  relations  for  the  plane,  he  asked  himself 
whether  they  were  analogous  to  those  for  free  fall.  This 
problem  resolves  itself  at  once  into  the  more  specific  one : 


152  THE  TEACHING  OF  PHYSICS 

Is  the  velocity  acquired  by  sliding  down  a  plane  the  same 
as  that  acquired  by  falling  freely  through  the  height  of 
the  plane  ? 

In  the  reply  to  this  question,  Galileo  reasoned  some- 
what as  follows : l  "  If  we  should  assume  that  a  body 
falling  down  the  length  of  an  inclined  plane  in  some  way 
or  other  attained  a  greater  velocity  than  a  body  that  fell 
through  its  height,  we  should  only  have  to  let  the  body 
pass  with  the  acquired  velocity  to  another  inclined  or 
vertical  plane  to  make  it  rise  to  a  greater  vertical  height 
than  it  had  fallen  from.  And  if  the  velocity  attained 
on  the  inclined  plane  were  less,  we  should  only  have  to 
reverse  the  process  to  obtain  the  same  result.  In  both 
cases  a  heavy  body  could,  by  an  appropriate  arrange- 
ment of  inclined  planes,  be  forced  continually  upwards 
solely  by  its  own  weight  —  a  state  of  things  which  wholly 
contradicts  our  instinctive  knowledge  of  the  nature  of 
heavy  bodies." 

Having  reached  this  conclusion  by  reasoning,  Galileo 
tried  his  well-known  experiment  with  the  large  pendulum, 
driving  nails  at  various  points  in  the  wall  so  as  to  catch 
the  string  of  the  pendulum  and  make  the  bob  rise  on  one 
side  along  an  arc  of  shorter  radius  than  that  of  the  arc 
along  which  it  descended.  In  this  way  he  proved  that 

1  Mach,  Science  of  Mechanics,  Engl.  Tr.  by  McCormack,  p.  135  (Chi- 
cago, Open  Court,  1893). 


THE  BIOGRAPHY  OF  PHYSICS  153 

his  intuition,  that  bodies  did  not  of  themselves  rise  to 
higher  levels,  was  correct.  The  experiment  is  seldom 
mentioned  in  elementary  texts ;  yet  it  is  one  of  the  fun- 
damental experiments  in  physics. 

55.  The  Causal  Principle.  —  It  is  clear  enough  that 
the  intuition  that  guided  Galileo  in  his  reasonings  on 
this  problem  was  that  of  the  impossibility  of  perpetual 
motion.  Mach  says : 1  "In  the  arguments  by  which 
Galileo  is  led  to  his  discoveries,  an  important  role  is 
played  by  the  principle  that  a  body  rises  because  of  the 
velocity  acquired  in  falling  to  exactly  the  same  height 
from  which  it  has  fallen.  This  principle,  which  appears 
frequently  and  with  perfect  clearness  in  the  writings  of 
Galileo,  is  but  another  form  of  the  principle  of  the  im- 
possibility of  perpetual  motion." 

Mach  then  shows  that  the  fundamental  and  tacit  as- 
sumption of  all  science  is  the  causal  principle,  which  is 
often  expressed  by  the  phrase  "  every  action  has  a  cause. " 
In  the  ancient  science,  it  was  final  and  absolute  causes 
that  were  sought.  Here  the  causal  principle  appears  in 
the  form  of  that  of  sufficient  reason ;  as  in  the  case  of 
Archimedes,  mentioned  on  page  119,  the  equal-arm  lever 
was  in  equilibrium  because  it  was  symmetrical  about  the 
axis,  and  we  can  see  no  reason  why  it  turns  one  way 

1  Mach,  Die  Geschichte  und  Wurzel  des  Satzes  von  der  Erhaltung 
der  Kraft,  2d  ed.,  p.  7  (Leipzig,  Earth,  1909). 


154  THE  TEACHING  OF  PHYSICS 

rather  than  the  other.  But  in  modern  physics  this 
causal  principle  appears  in  a  different  form.  It  mani- 
fests itself  as  a  deep-lying  intuition  that  every  phenome- 
non is  related  to  some  other  phenomenon.  As  Mach  puts 
it,  "  The  causal  principle  is  characterized  with  sufficient 
clearness  when  we  say  that  it  assumes  an  interdependence 
of  phenomena  among  one  another."  1 

Modern  physics,  then,  does  not  seek  final  causes,  but 
recognizes  that  phenomena  are  related  in  such  a  way 
that  when  a  change  is  wrought  in  one  group,  corre- 
sponding changes  occur  in  some  other  group.  It  is  the 
form  of  the  relation  between  two  groups  of  simultaneously 
changing  phenomena  that  modern  physics  seeks  to  de- 
termine ;  and  this  is  just  exactly  what  Galileo  did.  He 
found  the  form  of  the  function  that  expressed  the  relation 
between  distance  and  time  for  a  ball  rolling  down  the  in- 
clined plane,  and  that  which  expressed  the  relation  be- 
tween velocity  acquired  and  vertical  distance  of  fall  both 
for  bodies  falling  freely  and  for  bodies  falling  under  con- 
straint. Galileo  is  the  first  physicist  in  whose  work  this 
modern  view  of  the  causal  principle  appears  with  perfect 
clearness. 

56.  Perpetual  Motion.  —  But  this  is  not  all.  The 
recognition  of  the  relatedness  of  phenomena  appears 
in  another  intuition  which  is  really  the  guiding  star  of 

1  Mach,  Die  Geschichte  und  Wiirzel  des  Satzes  von  der  Erhaltung  der 
Kraft,  2d  ed.,  p.  35  (Leipzig,  Barth,  1909). 


THE  BIOGRAPHY  OF  PHYSICS  155 

modern  physics.  If  one  change  never  takes  place  in  one 
object  without  a  related  change  taking  place  in  some 
other  object  or  objects,  intuition  at  once  senses  the  im- 
possibility of  perpetual  motion.  This  is,  of  course,  no 
quantitative  proof;  it  is  but  a  qualitative  intuition, 
which  "  sees  the  goal  from  afar."  It  is  perfectly  clear 
that  Galileo  both  had  this  intuition  and  proved  it  quan- 
titatively for  the  special  case  of  bodies  falling  freely  or 
down  inclined  planes.  It  is  this,  more  than  anything 
else,  which  entitles  Galileo  to  his  position  as  founder  of 
dynamics.  His  discovery  of  the  fact  that  forces  deter- 
mine acceleration,  while  a  great  contribution  to  physics, 
as  distinguished  from  ancient  science,  is  not  as  important 
as  is  his  tacit  assumption  of  the  relatedness  of  phenomena 
and  the  consequent  intuition  of  the  impossibility  of  per- 
petual motion. 

One  other  important  point  in  Galileo's  work  is  his 
treatment  of  the  motion  of  projectiles.  In  this  case  his 
assumption  is  that  each  of  two  simultaneous  motions 
produces  the  same  effect  as  it  would  produce  if  taking 
place  alone,  i.e.  that  the  two  motions  are  really  inde- 
pendent, so  that  the  resultant  motion  may  be  found  by 
algebraically  adding  them. 

57.  Newton's  Work.  —  In  Newton  the  causal  princi- 
ple appears  in  full  brilliancy  in  the  modern  form.  For 
Aristotle  the  stone  fell  because  it,  acting  alone,  sought  its 


156  THE  TEACHING  OF  PHYSICS 

natural  place.  But  for  Newton  stone  and  earth  are 
related  bodies  which  determine  for  each  other  mutual 
accelerations.  His  extension  of  the  idea  of  mutual 
relationship  to  the  sun  and  planets  was  a  magnificent 
extension  of  the  relativity  idea,  and  brought  a  vast  range 
of  mechanical  phenomena  from  the  realm  of  intuition 
into  that  of  quantitative  proof  and  logic.  What  more 
explicit  statements  of  mutual  interdependence  could  be 
made  than  "  every  particle  in  the  universe  attracts  every 
other  particle,"  and  "  action  and  reaction  are  equal 
and  opposite  "  ? 

The  recognition  of  the  interdependence  of  phenomena 
seems  to  be  the  soul  of  Newton's  laws  of  motion.  The 
first  may  be  regarded  as  a  statement  of  the  fact  that  a 
wholly  isolated  or  independent  body  suffers  no  change  of 
motion.  The  third  tells  us  that  whenever  a  change  of 
motion  does  occur,  at  least  two  bodies  are  mutually  in- 
volved ;  and  the  second  and  third  together  exemplify 
the  spirit  of  modern  physics  by  giving  the  form  which  ex- 
presses the  relations  involved  in  the  mutual  action  of  two 
bodies,  namely,  the  momenta  are  equal  (mi  Vi  =  nh  *'2). 

The  greatness  of  Newton's  work  does  not,  however, 
consist  solely  in  the  fact  that  he  perceived  the  inter- 
dependence of  phenomena.  Because  he  was  able  to 
pick  out  those  characteristics  of  phenomena  that  could 
be  easily  measured  and  to  devise  expedient  methods 


THE  BIOGRAPHY  OF  PHYSICS  157 

of  measuring  them,  he  was  able  to  bring  his  perception  or 
intuition  of  relatedness  into  a  quantitative  form  in  which 
it  was  capable  of  verification.  As  has  been  noted,  Gali- 
leo determined  by  measurements  the  form  which  ex- 
presses the  relation  between  the  two  variables,  distance 
and  time,  for  bodies  rolling  down  an  inclined  plane,  and 
also  perceived  that  forces  were  related  to  accelerations. 
Newton  brought  this  perception  of  Galileo's  into  the 
realm  of  positive  and  quantitative  fact  by  introducing 
an  arbitrary  constant,  mass,  and  proving  by  numerous 
experiments  the  validity  of  the  form  force  =  mass  X  ac- 
celeration. 

This  form,  as  Newton  uses  it,  is  a  definition  of  the 
most  expedient  method  of  measuring  force.  In  it  mass 
becomes,  as  Poincare  shows, 1  a  "  coefficient  which  it  is 
convenient  to.  introduce  into  calculations."  This  rela- 
tion makes  force,  as  thus  defined,  the  center  of  the  New- 
tonian system,  and  leads  at  once  to  the  doctrine  of  cen- 
tral forces  and  to  momentum  as  the  measure  of  action 
and  reaction.  These,  then,  are  the  tools,  fashioned  by 
Newton,  with  which  physics  has  worked  for  more  than 
two  hundred  years.  Their  expediency  is  proven  beyond 
question  by  the  long  series  of  triumphs  which  have  been 
achieved  by  their  use,  especially  in  the  field  of  celestial 
mechanics,  where  there  is  no  friction. 

1  Poincar6,  Science  and  Hypothesis,  p.  76. 


158  THE   TEACHING  OF   PHYSICS 

But  if  Newton  possessed  the  intuition  of  the  relativity 
of  mechanical  processes,  he  gives  no  direct  evidence  of 
having  felt  the  impossibility  of  perpetual  motion.  The 
ideas  of  work  and  energy  are  difficult  to  discover  in  his 
Principia.  It  is  true,  that,  in  the  scholium  to  the  third 
law,  he  does  mention  the  equality  of  the  products  of  the 
weights  and  the  vertical  distances  on  the  two  sides  of  a 
lever  as  one  of  the  conditions  determinative  of  equilib- 
rium. But  he  makes  no  further  use  of  this  idea.  For 
the  problems  he  had  in  hand  his  definitions  and  axioms 
were  adequate  and  expedient. 

It  is  difficult  to  conceive  that  Newton  did  not  perceive 
that  perpetual  motion  is  impossible,  especially  since 
both  Galileo  and  Huyghens  had  already  made  such 
fruitful  use  of  the  intuition.  It  seems  far  more  probable 
that  he  did  perceive  it,  but  did  not  mention  the  fact, 
because,  with  the  science  of  heat  still  in  the  intuitive 
stage,  he  could  not  treat  it  in  the  same  rigorous  way  in 
which  he  treated  the  other  mechanical  relations,  action 
and  reaction,  for  instance.  It  may  be  that  he  was  so 
much  influenced  by  Descartes  and  by  the  fact  that 
momentum  is  conserved  in  impact  that  he  deliberately 
dismissed  work  as  an  unfruitful  idea.  Whatever  the 
reason  may  be,  it  is  clear  that  the  idea  of  work  plays  a 
negligible  role  in  Newton's  own  system  as  he  left  it. 

58.   Newton's  Successors.  —  But  if  Newton  himself 


THE  BIOGRAPHY  OF  PHYSICS  159 

failed  to  make  use  of  the  idea  of  work,  it  soon  came  to 
the  front  in  the  work  of  his  successors.  The  extension 
of  Newton's  principles  to  terrestrial  mechanics  soon  led 
to  the  discovery  of  general  principles  of  mechanics,  like 
D'Alembert's  principle  and  that  of  least  action.  But  all  of 
these  are  work  principles.  In  this  connection  Lagrange's 
proof  (1788)  of  the  principle  of  virtual  velocities  is  in- 
structive. He  conceives  all  the  forces  that  are  acting 
on  a  body  to  be  replaced  by  sets  of  pulleys  about  which 
one  continuous  cord  is  passed.  On  the  end  of  the  cord 
a  weight  is  hung.  The  number  of  sheaves  in  each  set 
of  pulleys  is  so  chosen  that  the  set  really  replaces  the 
force.  It  is  then  clear  that  equilibrium  results  when  the 
weight  cannot  descend.  In  other  words,  equilibrium 
results  because  heavy  bodies  do  not  of  themselves  as- 
cend. The  fundamental  assumption  here  is  again  the 
impossibility  of  perpetual  motion.  Lagrange  and  others 
have  tried  to  find  other  proofs  of  this  principle,  in  which 
this  assumption  is  not  made,  but  without  avail.1 

In  the  century  that  passed  between  the  publi cation  of 
Newton's  Principia  (1686)  and  Lagrange's  Mecanique 
Analytique  (1788)  the  genius  of  Europe  was  employed 
in  working  out  the  consequences  of  Newton's  definitions 
and  axioms.  Lagrange's  work  may  be  regarded  as  the 

1  For  a  full  discussion  of  this  point  see  Mach,  Science  of  Mechanics, 
p.  65  sq. 


160  THE  TEACHING  OF  PHYSICS 

completion  of  the  edifice  whose  foundations  were  laid  by 
Newton.  His  ideas  were  found  adequate  to  serve  as  a 
basis  for  celestial  and  analytical  mechanics;  taken  as 
mathematical  forms,  they  have  proved  fruitful  in  the 
extreme.  But  the  physical  content  of  these  forms  has 
always  been  a  matter  of  controversy  and  discussion.1 
A  comparison  of  the  methods  used  to  introduce  Newton's 
laws  of  motion  in  various  texts  shows  that  teachers  are 
not  agreed  at  present  as  to  just  what  they  mean.  The 
more  recent  texts  have  finally  come  down  to  introducing 
them  with  a  statement  like  this :  "  Over  two  hundred 
years  ago  Sir  Isaac  Newton  published  three  laws  of 
motion  which  were  generalizations  from  experimental 
data  and  facts  of  common  experience.  The  first  law 
is : "  etc. 

59.  Introduction  to  Mechanics.  —  It  is,  nevertheless, 
perfectly  clear  that  the  student  will  not  see  at  once  that 
they  are  generalizations  of  common  experiences.  He 
will  not  even  see  that  a  body  in  motion  continues  in 
motion  unless  stopped  by  some  force;  much  less  is  the 
measurement  of  force  by  acceleration  an  immediate 
percept  from  common  experience.  To  him  the  book 
on  the  table  weighs  just  as  many  pounds  when  it  is  at 
rest  as  it  does  when  it  is  in  motion ;  and  does  he  not  have 

1  For  example,  Pearson,  Grammar  of  Science,  Chapter  VIII,  2d  ed. 
(London,  Black,  1900). 


THE  BIOGRAPHY  OF  PHYSICS  161 

to  row  hard  in  a  boat  to  keep  it  moving  uniformly? 
Why,  then,  is  force  measured  by  acceleration?  These 
and  many  other  difficulties  of  like  nature  cluster  about 
the  teaching  of  these  laws  at  the  beginning  of  a  course  in 
physics.  The  trouble  seems  to  lie  in  the  fact  that  it 
requires  considerable  power  of  abstraction  to  grasp  the 
idea  that  these  laws  ignore  our  sensations  of  force  and 
give  us  no  information  about  what  mass  and  force  are, 
but  only  define  the  most  expedient  and  rigorous  way  of 
measuring  them.  These  laws  are  fundamental  to  a 
logical  and  rigorous  interpretation  of  mechanical  re- 
lations; but  there  is  a  yawning  chasm  between  the  in- 
tuitive and  anthropomorphic  interpretation  which  chil- 
dren bring  to  the  study  of  physics  and  the  analytical 
mechanics  of  Newton  and  Lagrange. 

There  can  be  little  doubt  that  from  the  point  of  view 
of  logic  and  rigor,  the  Newtonian  method  of  approach 
to  the  study  of  mechanics  is  an  excellent  one.  It  is 
also  evident  that  every  prospective  physicist  ought  to 
master  the  ideas  of  this  method  of  treating  mechanics. 
But  we  are  here  considering  the  use  of  physics  as  a 
means  of  general  education,  and  from  this  point  of  view 
it  may  well  be  doubted  whether  the  mere  statement  that 
these  laws  are  verified  by  all  our  common  experiences  will 
suffice  to  convert  the  anthropomorphic  conceptions  of 
youth  into  the  clear-cut  mathematical  conceptions  of 


162  THE  TEACHING  OF  PHYSICS 

analytical  mechanics.  Even  supplementing  the  state- 
ment by  citing  some  experiences  does  not  always  help 
to  clear  the  matter  up,  as  the  following  example,  intended 
to  clarify  the  matter  for  the  pupils,  will  show. 

In  one  of  the  latest  of  the  college  texts  of  physics,  the 
statement  of  Newton's  first  law  is  introduced,  as  it 
should  be,  by  reference  to  common  experiences.  Among 
those  mentioned  is  this:  "A  locomotive,  in  pulling  a 
train  with  uniform  velocity  along  a  level  track,  exerts  force 
sufficient  to  overcome  friction,  air  pressure,  etc.,  but 
no  more."  Then  follows  the  statement  of  the  first  law. 
After  this  we  read:  "  This  law  is  embodied  in  the  equa- 
tion F  =  Ma.  If  a  be  zero,  there  is  no  force."  With 
such  a  presentation,  how  can  the  student  fail  to  wonder 
which  statement  is  correct?  If  the  locomotive  exerts 
a  force  when  it  is  pulling  the  train  with  uniform  speed, 
when  a  =  o,  by  what  magic  has  the  introduction  of  the 
equation  suddenly  proved  that  there  is  no  force  ?  There 
is  no  explanation  of  the  anomaly  in  the  text,  and  so  the 
student  is  left  in  a  muddle,  torn  with  conflicting  emo- 
tions between  his  intuitive  perception  of  the  correctness 
of  the  first  statement  and  his  mathematical  sense  that 
the  equation  by  some  hocus  pocus  proves  the  second. 
This  muddle  is  liable  never  to  be  cleared  up,  excepting 
in  the  cases  of  a  few  of  those  who  are  hardy  enough  to 
go  on  into  advanced  physics  in  spite  of  it.  Yet  both 


THE  BIOGRAPHY  OF  PHYSICS  163 

statements  are  correct.  The  former  is  true  when  force 
is  defined  in  the  common-sense,  engineer's  way;  and 
the  latter  is  rigorously  true  when  denned  by  the  New- 
tonian definition.  It  is  doubtless  a  fine  thing  for  physics 
to  carry  the  student  over  from  one  definition  to  the  other, 
since  this  marks  an  advance  in  logic  and  in  abstraction. 
But  when  it  is  done  as  it  is  in  the  case  just  cited,  the 
students  may  well  exclaim,  "  Oh,  George !  but  this  is 
so  sudden !  " 

60.  The  Advent  of  the  Steam  Engine.  —  But  to 
return  to  the  biography  of  physics:  as  has  been  noted, 
there  was  little  done  in  physics  during  the  century  fol- 
lowing the  publication  of  the  Principia.  We  find  a 
number  of  men  experimenting  with  static  electricity,  but 
the  majority  of  those  who  were  mathematically  inclined 
were  studying  Newton  and  perfecting  the  celestial  and 
analytical  mechanics  to  which  he  made  such  brilliant 
contributions. 

Towards  the  end  of  the  century,  physics  proper  began 
to  revive.  A  new  era  may  be  said  to  begin  with  the  in- 
vention of  the  steam  engine  by  James  Watt  (1789).  It 
was  this  invention  and  the  studies  that  Watt  made  in 
heat  that  turned  the  attention  of  the  physicists  in  this 
direction.  For  the  purpose  of  this  discussion  it  is  not 
necessary  to  follow  the  development  of  thermodynamics 
in  detail  through  the  work  of  Rumford  and  others  down 


1 64  THE  TEACHING  OF  PHYSICS 

to  Sadi  Carnot.  It  is  with  the  investigations  of  Carnot, 
J.  R.  Mayer,  and  Joule  that  we  are  particularly  con- 
cerned. 

Carnot's  brief  treatise  (Reflections  sur  la  puissance 
motrice  du  feu,  Paris,  1824)  marks  the  beginning  of  this 
reduction  of  a  second  great  domain  of  physics  from  the 
realms  of  intuition  and  perception  to  those  of  logic  and 
law.  The  gist  of  Carnot's  work  lies  in  his  demon- 
stration that  for  a  given  amount  of  work  the  quantity 
of  heat  that  flows  from  the  higher  temperature  t  to  the 
lower  temperature  t\  does  not  depend  on  the  nature  of 
the  working  substance,  but  only  on  the  range  of  tem- 
perature. He  reaches  this  conclusion  because,  if  it  is 
not  true,  a  combination  of  bodies  could  be  imagined 
which  would  enable  us  to  produce  work  continually 
from  nothing.  Thus  here  again,  the  intuition  that 
perpetual  motion  is  impossible  pointed  the  way  to  the 
goal.  The  fact  that  Carnot's  demonstration  is  faulty 
does  not  alter  this  argument,  since  his  principle  is  correct, 
as  was  shown  later  by  Kelvin  by  a  different  method.1 

61.  The  Conservation  of  Energy.  —  The  importance 
of  Carnot's  work  for  the  present  day  physics  no  one 
denies.  His  cycle,  his  principle,  and  his  ideas  of  re- 
versible and  irreversible  processes  started  a  long  line  of 

1  For  a  fuller  discussion  see  Magie,  The  Second  Law  of  Thermodynam- 
ics (New  York,  Harper,  1899). 


THE  BIOGRAPHY  OF  PHYSICS  165 

most  fruitful  investigations.  When  complemented  by 
the  investigations  of  Mayer,  Joule,  and  Helmholtz,  they 
not  only  brought  heat  under  the  sway  of  measurement, 
but  also  showed  that  there  was  a  constant  ratio  between 
the  conventional  work  unit  of  mechanics  and  that  of 
quantity  of  heat ;  namely,  i  British  Thermal  Unit  = 
778  foot  pounds. 

The  electrical  unit,  the  watt-second,  soon  yielded  to 
the  same  treatment,  and  was  found  to  bear  a  constant 
ratio  to  the  unit  of  heat  quantity.  Whenever  the  ratio 
between  two  units  is  constant,  we  know  that  the  units 
are  different  units  for  measuring  the  same  thing.  This 
same  thing,  which  may  be  measured  in  foot  pounds,  in 
British  Thermal  Units,  or  in  watt-seconds,  is  called 
energy.  Therefore,  because  of  this  constancy  of  the 
ratios  between  various  pairs  of  these  units,  the  doctrine 
of  the  conservation  of  energy  became  a  necessity. 

It  is  important  to  note  in  this  connection  that  the 
principle  of  the  conservation  of  energy  does  not  assert 
that  the  sum  total  of  all  the  energy  in  the  universe  is 
constant.  In  this  form  it  would  sound  well,  but  be 
practically  useless.  What  it  does  tell  us  is  that  there 
are  constant  relations  between  the  units  by  which  we 
measure  mechanical  work,  quantity  of  heat,  and  elec- 
trical work,  i.e.  between  the  foot  pound,  the  British 
Thermal  Unit,  and  the  watt-second  (or  the  erg,  the 


1 66  THE  TEACHING   OF  PHYSICS 

gram  calorie,  and  watt-second).  Because  of  these  con- 
stant ratios,  it  is  possible  to  reduce  all  units  of  measure- 
ment to  those  of  mechanics.  In  other  words,  the  doc- 
trine of  energy  supplies  us  with  a  common  terminology 
and  a  common  system  of  units  for  all  branches  of  physics. 
It  thus  unifies  the  definitions  of  physics,  since  a  defini- 
tion is  of  little  use  in  physics  unless  it  tells  how  the  quan- 
tity defined  is  measured. 

62.  Energy  in  Physics  and  in  Industry.  —  At  present 
we  may  say  that  this  guiding  intuition  of  physics,  this 
sense  of  the  impossibility  of  perpetual  motion,  this 
recognition  of  the  relatedness  of  physical  phenomena,  has 
become  pretty  well  incarnated  in  the  realms  of  law  and 
logic.  If  at  first  it  was  but  a  vague  and  half-conscious 
intuition,  it  has  now  become  a  very  real  and  well- 
established  fact.  And  it  is  interesting  to  note  that  the 
name  given  to  that  constant  something  which  is  measured 
either  in  foot  pounds,  in  B.  T.  U.,  or  in  watt-seconds 
is  the  same  as  that  given  to  that  conscious  something  in 
terms  of  which  the  accounts  of  the  world  are  settled  — 
energy.  The  man  of  commerce  may  think  that  the 
world's  accounts  are  settled  by  money;  but  the  stu- 
dent of  real  physics,  —  of  physics  as  it  is,  as  distinguished 
from  physics  of  the  schools,  —  he  knows  that  energy  is 
the  final  basis  of  industrial  values. 

It  can  hardly  be  by  chance  that  physics  and  the  world 


THE  BIOGRAPHY  OF  PHYSICS  167 

of  commerce  and  industry  both  use  the  same  idea  as  the 
idea  that  unifies  their  standards  of  value.  But  since  it 
is  so,  why  not  make  the  vast  range  and  variety  of  ex- 
periences, which  every  one  has  accumulated  about  the 
ideas  of  energy,  the  starting  points  for  the  problems  of 
physics?  Why  is  it  considered  necessary  to  make  a 
detour  through  the  elements  of  analytical  and  celestial 
mechanics  before  starting  in  on  real  physics?  Any  one 
who  can  measure  in  pounds  and  feet,  and  who  can  read 
a  thermometer,  a  voltmeter,  and  an  ammeter,  can  begin 
to  make  measurements  in  energy.  He  can  even  measure 
the  pull  of  the  engine  on  the  uniformly  moving  train  in 
pounds,  though  its  value  be  zero  in  dynes !  He  can  in 
this  way  become  interested  in  the  physical  world  about 
him,  can  begin  to  organize  his  vast  range  of  associated 
experiences  about  the  fundamental  ideas  of  physics, 
and  by  and  by  he  may  even  be  able  to  sail  off  into 
space  and  find  joy  in  applying  the  analytical  and  celes- 
tial mechanics  to  determining  the  perturbations  of  minor 
planets  or  the  orbit  of  the  tenth  satellite  of  Jupiter. 

63.  Work  Precedes  Logic.  —  It  is  important  to  note 
in  closing  that  the  foregoing  argument  in  favor  of  be- 
ginning the  study  of  physics  with  considerations  of 
energy  relations  makes  no  mention  of  the  question 
whether  the  Newtonian  or  the  Energetic  school  of 
physics  is  preferable.  This  problem  is  one  which  is 


1 68  THE  TEACHING  OF  PHYSICS 

still  in  process  of  solution.  That  may  turn  out  to  be 
quite  a  different  story.  Fortunately,  it  has  little  bear- 
ing on  the  problem  of  using  physics  for  purposes  of  gen- 
eral education.  Beginning  with  ideas  of  work  is  advo- 
cated because  work  measured  in  foot  pounds  is  a  con- 
crete idea  which  is  easily  grasped  by  most  young  people 
and  which  is  also  already  associated  in  their  minds  with 
a  very  wide  range  of  experiences.  It  is  easy  to  lead  from 
studies  of  the  efficiencies  of  simple  machines  on  to  the 
Newtonian  mechanics  if  the  teacher  wishes  to  do  this. 
Since  this  is  at  present  the  best-established  form,  it  will 
probably  be  safe  to  continue  to  do  this  for  the  present. 

The  logical  is,  nevertheless,  always  the  goal  toward 
which  the  instruction  is  aimed;  but  the  imposition  of 
the  logical  on  the  student  at  the  very  start  is  fatal  to 
the  success  of  the  whole  undertaking.  He  must  be  led 
from  things  that  are  to  him  concrete  on  to  the  abstract. 
In  this  he  follows  in  a  vague  sort  of  a  way  the  general 
development  of  physics.  Since  the  motive  of  this  de- 
velopment has  been  the  feeling  for  relatedness  and  the 
intuition  of  the  impossibility  of  perpetual  motion,  these 
elements  should  be  prominent  at  the  beginning  as  well 
as  all  through.  The  purpose  is  to  bring  these  intuitions 
from  the  sphere  of  the  vague  and  indefinite  into  the 
realm  of  the  concrete  and  the  logical. 


THE  BIOGRAPHY  OF  PHYSICS  169 

SUPPLEMENTARY  READING 

MACH,  E.     The  Science  of  Mechanics.    Chicago,  Open  Court, 
1893. 

Die  Geschichte  und  Wiirzel  des  Satzes  von  der  Erhaltung  der 

Kraft.     2d  ed.    Leipzig,    1910.     An    English  translation  is 
just  announced.    London,  Kegan  Paul,  1911. 

HERZ,  H.     The   Principles   of  Mechanics.     Introduction.    New 

York,  Macmillan,  1899. 
WARD,  JAMES.    Naturalism  and  Agnosticism,  Vol.  I,  Lectures  1-7. 

New  York,  Macmillan,  1899. 

LE  BON.     The  Evolution  of  Forces.    New  York,  Appleton,  1908. 
STALLO,  J.  B.     The  Concepts  and  Theories  of  Modern  Physics. 

New  York,  Appleton,  1897. 
POINCARE,   H.     Science  and  Hypothesis,   Chapters  VI-X,  XII- 

XIII,  and  Appendix. 

The  Value  of  Science,  Chapters  VII-IX. 

DUHEM,  P.    L*  Evolution  de  la  Mecanique.    Paris,  Hermann,  1905. 

Les  Origines  de  la  Statique.     Paris,  Hermann,  1905. 

BLOCK,  L.    La  Philosophic  de  Newton,  Chapters  IV-VIII.     Paris, 

Alcan,  1908. 
SCHUSTER,  A.     The  Progress  of  Physics  during  Thirty-three  Years,  y 

Cambridge  University  Press,  1911. 
ROSENBERGER,  F.    Isaac  Newton  und  seine  Physikalischen  Prin- 

cipien.    Leipzig,  Earth,  1895. 
OSTWALD,  W.    Die  Energie.    Leipzig,  Earth,  1908. 
PLANCK,  M.    Das  Princip  von  der  Erhaltung  der  Energie.    2d  ed. 

Leipzig,  Teubner,  1908. 
PEARSON,    K.    Grammar    of  Science,    Chapter    VIII.     London, 

Black,  1900. 
REY,  A.    UEnergetique  et  le  Mecanisme.    Paris,  Alcan,  1908. 


CHAPTER  VIII 
THE  DISCIPLINE  OF  PHYSICS 

64.  The  Doctrine  of  Formal  Discipline.  —  On  pages 
34  and  36  two  passages  are  quoted,  one  from  an  old 
textbook  of  natural  philosophy  (1846),  and  the  other  from 
a  recent  textbook  of  physics  (1902).  These  passages 
illustrate  the  change  that  took  place  in  the  methods  of 
treating  physics  during  the  interval  between  the  publi- 
cation of  the  first  and  that  of  the  second  book.  This 
change  from  one  form  of  treatment  to  the  other  was 
brought  about  by  two  main  causes;  one  was  the  rapid 
development  of  university  physics,  and  its  gradual  soak- 
ing down  into  the  schools  from  above;  and  the  other 
was  the  prevailing  educational  doctrine,  which  reached 
its  final  statement  in  the  Report  of  the  Committee  of 
Ten.  In  the  preceding  three  chapters  an  attempt  has 
been  made  to  define  the  real  nature  of  the  first  of  these 
causes;  it  remains,  therefore,  to  consider  the  meaning 
of  the  second. 

The  doctrine  of  formal  discipline  is  very  old.  It 
was  implied  in  the  educational  practices  of  the  Greeks 
and  the  Romans.  It  was  not,  however,  until  the  age 

170 


THE  DISCIPLINE  OF  PHYSICS  171 

of  scholasticism  that  it  appeared  as  a  consciously  formu- 
lated principle  of  education.  "  All  one  needed  was 
training  in  logic,  in  intellectual  gymnastics,  and  from 
this  source  of  knowledge,  the  inner  consciousness,  could 
be  spun  all  good  and  worthy  things."  *  Its  close  kin- 
ship with  Platonic^thought  is  worthy  of  note.  Physics 
was  taught  in  medieval  universities  under  the  influence 
of  this  doctrine.  It  consisted  in  endless  hair-splitting 
disputations  concerning  the  meanings  of  Aristotle's 
speculations.  Observation  and  experiment,  as  well  as 
emotion  and  feeling,  were  totally  overlooked.  The  stu- 
dents were  to  learn  physics,  not  by  studying  the  physical 
phenomena  about  them,  but  by  doing  something  else; 
namely,  by  juggling  with  words  and  meaningless  state- 
ments called  by  them  definitions. 

The  doctrine  came  to  be  still  more  explicitly  defined 
about  the  middle  of  the  eighteenth  century,  when  the 
exclusive  study  of  the  classics  in  schools  began  to  be  at- 
tacked by  a  public  hungering  for  a  real  education.  It 
was  then  that  the  schoolmen  flew  to  the  defense  of  the 
classics  with  a  more  explicit  statement  of  the  doctrine. 
The  essence  of  this  doctrine  is  thus  given  by  Monroe 2: 
"  The  mind  as  a  bundle  of  faculties  was  to  be  developed 

Bennett,  Formal  Discipline,  p.  9  (Teachers  College,  New  York,  1907). 

2  Monroe,  Text-book  in  the  History  of  Education,  pp.  505  sq.  (Macmillan, 
I9°5)-  Quoted  by  Heck,  Mental  Discipline,  p.  13  (20!  ed.,  New  York, 
Lane,  1911). 


172  THE  TEACHING  OF  PHYSICS 

by  exercising  these  various  powers  upon  appropriate 
tasks  whose  value  consisted  in  the  difficulties  they  offered. 
These  faculties  were  considered  to  have  no  necessary 
connection  with  one  another,  hence  these  disciplines 
were  separate  and  distinct  things;  though  some  facul- 
ties were  higher  than  others.  The  highest  was  the  rea- 
soning power  to  be  developed  by  appropriate  discipline 
in  mathematics,  logical  disputations,  and  the  languages ; 
but  the  faculty  upon  which  all  the  others  depended,  and 
upon  the  successful  development  of  which  depended  the 
success  of  the  education,  was  the  memory.  Discipline 
of  the  memory,  then,  took  precedence  above  all  other 
exercises.  The  best  training  for  the  memory  was  af- 
forded by  the  mastery  of  material  which  had  no  inherent 
interest  for  the  child." 

This  defense  of  education  by  classics  alone  on  the 
ground  of  their  peculiar  fitness  to  give  "  mental  dis- 
cipline "  has  persisted  with  strange  pertinacity  down  to 
the  present  time.  -  When  the  last  great  reaction  against 
confining  education  to  a  study  of  the  classics  alone  began, 
shortly  after  the  Civil  War,  about  1870,  the  position 
taken  by  the  schoolmen  of  the  eighteenth  century  was 
appealed  to  again  with  great  effect. 

65.  The  Work  in  Modern  Languages.  —  The  effect 
of  thus  defending  the  classics  on  grounds  of  mental  dis- 
cipline, instead  of  on  grounds  of  inherent  literary  worth, 


THE  DISCIPLINE  OF  PHYSICS  173 

has  been  disastrous  both  to  the  classics  themselves  and 
to  the  newer  subjects  that  were  striving  to  displace  them. 
Thus  when  the  demand  came  from  the  people  for  living 
instead  of  dead  languages,  these  new  aspirants  for  aca- 
demic honors  were  required  to  attack  the  classics  in  their 
fortification  of  mental  discipline.  French  and  German 
found  the  fortress  well-nigh  impregnable,  and  were  at 
last  compelled  to  erect  fortifications  of  their  own.  They 
did  this  by  copying  the  methods  of  the  classics,  reducing 
the  study  of  the  modern  languages  to  grammatical  analy- 
sis, parsing,  and  learning  of  paradigms.  That  was  the 
way  the  classics  secured  "  mental  discipline,"  hence 
the  moderns  must  do  likewise. 

Even  English  fell  a  victim  to  the  craze,  and  editions 
of  Shakespeare  and  of  other  "  English  classics  "  began 
to  appear  in  which  the  text  occupied  often  less  than 
half  the  book  and  the  "  explanatory  notes  "  and  guides 
to  parsing  took  up  the  rest.  The  inevitable  result  fol- 
lowed. Young  people  no  longer  read  Shakespeare  for 
the  pleasure  and  the  culture  that  comes  from  absorbing 
the  world's  great  literary  masterpieces.  The  writing 
of  "  English  themes  "  is  often  one  of  the  hardships  of 
life ;  —  all  because  English  set  off  on  a  wild-goose  chase 
after  mental  discipline  as  used  by  the  classics  for  self- 
defense  in  this  their  last  memorable  struggle.  English 
teachers  have  recently  waked  up  to  the  truth  of  Dewey's 


174  THE  TEACHING  OF  PHYSICS 

remark,   "  There  is  a  great  difference  between  having 
to  say  something,  and  having  something  to  say." 

66.  Formal   Discipline   in   Science.  —  Not   only  the 
languages,  but  the  sciences  as  well,  and  even  manual 
training,  fought  their  way  into  the  schools  on  the  ground 
that  they  furnished  "  mental  discipline  "  and  so  con- 
tributed to  "  culture."     For  the  Platonic  notion  that 
thinking  isaserjarate  and  distinct  function  of  life,  and, 
therefore^  that  intellectual  training  is  the  sole  end  of 
education,  was  everywhere  accepted  without  question. 
Science  and  manual  training  might  never  have  been 
able  to  break  into  the  academic  hierarchy  of  mental 
discipline  if  they  had  sought  entrance  on  their  own  legit- 
imate grounds  of  practical^  utility  and  the  training  of 
the  whole  boy  to  usefulness  in  life.     And  when  they  did 
gain  admission,  they  at  once  went  to  work  to  make  good 
and  prove  that  they  could  give  mental  discipline  of  the 
good  old  orthodox  kind,  with  all  its  methods  of  morti- 
fication of  the  will  for  the  glory  of  the  intellect. 

67.  Peculiarities  of  the  Doctrine.  —  There  are  sev- 
eral curious  features  of  the  doctrine  of  mental  discipline 
which  are  as  hard  to  understand  now  as  is  the  doctrine 
of  infant  damnation.     One  is  the  claim  that  it  is  impos- 
sible to  learn  to  speak  -  English  well  without  having 
studied  Latin.     In  other  words,  the  child  learns  to  do 
one  thing  by  doing  something  else.     By  the  same  token 


THE  DISCIPLINE  OF  PHYSICS  175 

he  learns  to  understand  his  present  surroundings  by  / 
studying  an  ancient  history  consisting  mainly  of  a  list 
of  emperors  with  the  dates  of  their  wars.  When  physics 
came  under  the  sway  of  this  idea,  it  soon  became  changed 
in  the  way  shown  in  the  quotations  on  pages  34-37 ; 
that  is,  if  you  want  the  pupils  to  learn  physics,  you  should 
teach  them  pure  mathematics. 

Another  of  the  curious  features  of  the  doctrine  is  its 
insistence  that  certain  specified  kinds  of  subject  matter 
are  inherently  endowed  with  the  power  of  giving  mental 
discipline  to  those  who  merely  rub  up  against  them  for  a 
given  length  of  time.  These  preeminently  disciplinary 
subjects  are  those  mentioned  on  page  12,  and  proclaimed 
by  the  Committee  of  Ten  as  being  "  proper  for  secondary 
schools."  The  belief  in  the  necessary  truth  of  this  idea 
is  still  prominent  among  the  public  at  large.  Many  a 
poor  girl  at  present  sacrifices  her  opportunities  for  a  real 
education  in  domestic  science  or  horticulture  for  a  school- 
ing in  Latin  and  algebra,  under  the  impression  that  she 
is  thereby  winning  admission  to  an  intellectual  caste 
in  which  alone  she  will  be  happy.  On  close  analysis  the 
evidence  for  the  necessary  truth  of  this  idea  is  found  to 
be  the  same  as  that  for  the  necessary  truth  of  the  ideas 
of  geometry,  as  mentioned  on  page  146 ;  namely,  the 
repugnance  which  the  mind  feels  to  changing  old  and 
deep-seated  prejudices. 


176  THE  TEACHING  OF  PHYSICS 

The  college  entrance  requirements  are  founded  on 
this  idea.  It  makes  no  difference  whether  a  student  is 
really  able  to  do  the  work  required  of  him  in  college; 
if  he  has  not  "  had  "  foreign  languages,  mathematics, 
and  English  as  taught  in  the  schools  under  college  super- 
vision, he  is  not  a  fit  subject  for  college.  The  effect 
is  perfectly  normal.  The  student  is  "  immune "  to 
these  subjects  in  college ;  very  much  as  he  is  immune  to 
the  measles,  or  any  other  disease  of  childhood,  after  he 
has  once  "  had  "  them. 

68.  Formal  Discipline  in  Physics.  —  The  effect  of 
these  ideas  on  physics  i?  so  clear  that  he  who  runs  may 
read.  Physics  is  usually  given  in  the  third  or  fourth 
years  of  the  high  school  so  that  the  pupil  may  have 
"  had "  algebra  and  geometry  before  coming  to  the 
physics.  Physics  must -be  taught  by  teaching  some- 
thing else;  namely,  mathematics.  The  physics  teachers 
then  wonder  why  the  pupils  do  so  poorly  in  "  physics  " 
and  complain  bitterly  that  the  students  cannot  do 
"  physics "  because  they  know  no  mathematics.  In 
reality  the  thing  is  perfectly  normal ;  they  have  "  had  " 
mathematics  and  so  are  immune. 

Under  these  conditions  the  mathematics  teachers 
have  attempted  to  assist  the  physics  teachers  by  cor- 
relating physics  with  mathematics.  In  one  recent  text 
in  which  the  authors  claim  to  have  done  this,  there  are 


THE  DISCIPLINE  OF  PHYSICS  177 

found  a  few  equations  from  physics,  like  s  =  J  a/2,  which 
are  introduced  with  some  remark  about  their  being 
equations  often  met  with  in  physics,  and  then  solved 
like  any  other  equations  in  algebra.  The  fallacy  of 
this  procedure  is  perfectly  clear ;  the  train  of  reasoning 
is  incomplete,  since  every  complete  train  of  thought 
must  begin  and  end  in  the  concrete. 

In  the  case  of  physics,  this  doctrine  is  well  named  that 
of  "  formal  "  discipline,  since  it  has  led  physics  to  attempt 
to  give  discipline  by  forcing  a  study  of  "  form  "  with 
little  content.  Newton  started  the  habit  by  presenting 
his  Principle,  in  geometrical  form  and  order  a  la  Euclid, 
because  he  was  too  sensitive  to  take  pleasure  in  friendly 
scraps  with  his  colleagues.  It  is  perfectly  clear  that 
the  "  forms  "  which  Newton  sets  up  had  content  to  him ; 
and  it  is  equally  clear  that  they  do  not  have  content  to 
high  school  pupils,  until  they  have  passed  through  a 
long  series  of  well-planned  experiences  and  experiments 
which  begin  in  situations  which  are  concrete  to  them 
and  gradually  lead  up  to  the  establishment  of  the  de- 
sired form.  Hence  physics,  in  its  efforts  to  give  "  dis- 
cipline "  in  accordance  with  the  old  doctrine  of  formal 
discipline,  has  floated  off  into  a  world  of  forms,  totally 
oblivious  to  Lincoln's  statement  that  a  man's  legs  should 
be  long  enough  to  reach  to  the  ground.  It  may  be  said 
to  have  given  lots  of  "  discipline,"  if  the  word  is  used 


178  THE  TEACHING  OF,  PHYSICS 

in  the  sense  of  punishment ;  for  the  harder  the  job  and 
the  greater  the  pupil's  aversion  to  it,  the  greater  was  its 
value  for  discipline.  Its  religion  has  been :  "  the  heavier 
the  cross,  the  brighter  the  crown." 

69.  Psychology  to  the  Rescue.  —  But  a  new  day  is 
dawning  for  the  school  children.  The  science  of  psy- 
chology is  coming  to  their  rescue,  by  proving  that  the 
human  mind  is  not  made  up  of  separate  faculties  of 
which  reason  and  memory  are  the  chiefs.  Thinking 
is  no  longer  an  isolated  function,  set  off  by  itself  in  a 
celestial  region  of  frigid  bliss.  It  is  part  of  a  process  in 
which  the  whole  mind  is  engaged,  including  the  volitions, 
emotions,  imaginations,  tastes,  aversions,  and  the  rest. 
The  mind  no  longer  has  a  separate  thought-tight  com- 
partment called  memory,  another  called  reason,  and  an- 
other called  imagination,  and  so  on.  Instead,  each  mind, 
acting  as  a  whole,  has  memories,  reasonings,  and  imag- 
inations. In  the  words  of  Thorndike : 1  "  The  mental 
sciences  should  at  once  rid  themselves  of  the  conception 
of  the  mind  as  a  sort  of  machine,  different  parts  of  which 
sense,  perceive,  discriminate,  imagine,  remember,  con- 
ceive, associate,  reason  about,  desire,  choose,  form 
habits,  attend  to.  Such  a  conception  was  adapted 
to  the  uses  of  writers  of  books  on  general  method  and 

1  Thorndike,  Educational  Psychology,  p.  187  (New  York,  Teachers  Col- 
lege, 1910). 


THE  DISCIPLINE  OF  PHYSICS 


179 


arguments  for  formal  discipline  and  barren  descriptive 
psychologies,  but  such  a  mind  nowhere  exists.  There 
is  no  one  power  of  sense  discrimination  to  be  delicate  or 
coarse,  no  capacity  for  uniform  accuracy  in  judging  the 
physical  stimuli  of  the  outside  world.  There  are  only 
the  connections  between  sense  stimuli  and  our  separate 
sensations  and  judgments  thereof,  some  resulting  in 
delicate  judgments  of  difference,  some  resulting  in  coarse 
judgments.  There  is  no  one  memory  to  hold  in  a  uni- 
formly tight  or  loose  grip  all  the  experiences  of  the  past. 
There  are  only  the  particular  connections  between 
particular  mental  events  and  others,  sometimes  result- 
ing in  a  great  surety  of  revival,  sometimes  in  little.  And 
so  on  through  the  list.  Good  reasoning  power  is  but  a 
general  name  for  a  host  of  capacities  and  incapacities, 
the  general  average  of  which  seems  to  the  namer  to  be 
above  the  general  average  in  other  individuals." 

70.  The  Problem  of  Transfer  of  Training.  —  This 
radical  change  of  base  has  opened  up  a  large  field  of  in- 
vestigation. If  reasoning  is  no  longer  the  isolated  activ- 
ity of  a  special  faculty  of  the  mind,  but  is  the  result  of  a 
very  complex  and  varied  interaction  of  many  elements, 
it  no  longer  follows  that  a  mind  trained  to  reason  well 
in  geometry  will  reason  well  in  economics.  The  other 
elements  that  interact  in  the  reasoning  process  may  be 
very  different  in  the  one  case  from  what  they  are  in  the 


l8o  THE  TEACHING  OF  PHYSICS 

other.  Therefore,  it  is  by  no  means  a  self-evident  fact, 
as  the  doctrine  of  formal  discipline  assumes  it  to  be,  that 
reasoning  in  geometry  develops  an  abstract  or  general- 
ized power  of  reasoning  which  will  be  of  equal  service  in 
any  other  field.  In  fact,  common  experience  shows  this 
not  to  be  so,  since  mathematicians  are  by  no  means  the 
most  acute  and  skillful  reasoners  on  questions  of  finance, 
politics,  business  management,  and  the  like.  The  ab- 
sent-minded and  impractical  college  professor  has  be- 
come a  standing  joke. 

But  if  it  is  certain  that  training  in  reasoning  in  geome- 
try does  not  necessarily  result  in  developing  general 
powers  of  reasoning,  it  is  equally  certain  that  many 
student  of  geometry  do  gain  from  that  study  something 
which  strengthens  their  mental  fiber  and  clarifies  their 
mental  operations.  Hence  the  great  problem  for  edu- 
cational psychology  is  to  find  out  under  what  conditions 
training  in  one  kind  of  activity  results  in  increased  power 
of  dealing  with  some  other  kind  of  activity.  To  be 
specific,  if  the  greatest  use  of  physics  in  education  is  to 
assist  in  developing  among  the  pupils  at  large  a  scientific 
attitude  of  mind  in  dealing  with  all  their  problems,  the 
physics  teacher  must  understand  the  conditions  under 
which  the  specific  training  given  in  the  physics  class 
results  in  general  ability  to  deal  scientifically  with  specific 
problems  in  other  fields  than  that  of  physics. 


THE  DISCIPLINE  OF  PHYSICS  181 

This  is  an  extremely  complex  and  difficult  problem. 
It  involves  a  careful  study  not  only  of  the  relations  be- 
tween any  given  subject  matter  and  the  environment  of 
the  school,  but  also  of  the  individual  differences  of  the 
pupils,  and  "  the  respective  shares  which  sex,  age,  '  race  ' 
or  remote  ancestry,  '  family '  or  immediate  ancestry, 
and  the  circumstances  of  life  have  in  the  causation  of 
such  differences.  What  we  think  and  what  we  do  about 
education  is  certainly  influenced  by  our  opinions  about 
such  matters.  .  .  .  For  example,  manual  training  is 
often  introduced  into  the  schools  on  the  strength  of 
somebody's  confidence  that  skill  in  movement  is  inti- 
mately connected  with  efficiency  in  thinking.  The 
American  school  system  rests  on  a  total  disregard  of 
hereditary  mental  differences  between  the  classes  and 
the  masses;  curricula  are  planned  with  some  specula- 
tion concerning  mental  development  as  a  guide."  1 

But  as  in  physics,  so  in  psychology,  "  effective  de- 
scription of  the  facts  of  individual  differences  and  of 
their  causation  must  be  quantitative.  The  questions  are 
questions  of  amount,  or  at  least  become  such  when  carried 
beyond  the  first  survey.  '  Do  boys  and  girls  differ  ?  '  is 
itself  a  question  of  amount,  which  soon  becomes,  '  How 
much  do  boys  and  girls  differ?  '  '  In  what  do  they  dif- 
fer? '  and  can  be  answered  only  by  comparing  them 

1  Thorndike,  Educational  Psychology,  p.  i  (New  York,  Teachers  College, 
1910). 


182  THE  TEACHING  OF  PHYSICS 

quantitatively.  .  .  .  'What  is  the  value  of  Latin?' 
means  to  even  the  student  most  averse  to  quantitative 
thinking,  '  What  changes  in  human  nature  are  caused 
by  it?'  But  to  prove  the  existence  of  any  change, 
one  must  measure  two  conditions."  1 

Thorndike  then  goes  on  to  explain  the  specific  problems 
that  arise  when  one  undertakes  to  make  quantitative 
measurements  of  individual  differences,  and  gives  numer- 
ous examples  in  which  such  quantitative  data  have  been 
obtained.  This  science  of  psychology  is,  however,  still 
in  its  infancy.  It  needs  a  Newton  to  give  mathematical 
form  to  the  definitions  of  this  "  spiritual  mechanics." 
Thorndike  concludes  (p.  192) :  "  Just  what  the  origi- 
nal relations  are,  will  in  the  progress  of  research  be  dis- 
covered. But  present  knowledge  is  insufficient  to  deter- 
mine even  the  original  relations." 

71.  Training  is  Specific.  —  Even  though  our  present 
knowledge  is  not  sufficient  for  this  purpose,  there  are  a 
number  of  working  hypotheses,  which  have  been  ad- 
vanced by  the  advocates  of  the  new  doctrine,  and  which 
have  proved  themselves  to  be  both  suggestive  and  fruit- 
ful to  teachers.  The  rest  of  this  chapter  will  be  devoted 
to  stating  those  hypotheses  and  ideas  that  seem  to 
promise  most  for  the  teachers  of  physics ;  their  problem 
being  to  find  out  how  to  give,  by  their  instruction  in 

1  Thorndike,  Educational  Psychology,  p.  2  (New  York,  Teachers  College, 
1910). 


THE  DISCIPLINE  OF  PHYSICS  183 

physics,  a  training  that  shall  be  of  the  greatest  possible 
value  for  purposes  of  general  education. 

The  first  point  to  be  noted  is  that  training  in  any  sub- 
ject is  specific,  not  general.  Much  of  the  vagueness  of 
the  older  doctrine  lies  in  the  fact  that  it  assumes  that 
training  in  general  is  possible.  The  Greeks  and  others 
have  made  the  same  mistake  about  thinking,  assuming 
that  thinking  is  some  sort  of  a  general  activity  whose  laws 
and  principles  could  be  established  in  general.  But 
thinking,  like  training,  is  always  specific,  i.e.  connected 
with  some  particular  situation  and  dependent  upon  the 
specific  nature  of  the  situation  as  a  whole.  In  order  to 
induce  a  student  to  think,  it  is  necessary  to  place  him  in 
a  definite  situation  which  necessitates  his  thinking.  In 
like  manner  discipline  is  best  secured  not  by  imposing 
artificial  tasks  or  formal  routines  inherently  distasteful 
to  the  pupil,  but  by  creating  a  specific  situation  from 
which  discipline  results. 

The  fundamental  education  of  man  was  secured  from 
his  relations  with  nature  ages  before  schools  were  in- 
vented ;  yet  nature  never  forces  on  men  problems  that 
are  just  made  up  to  be  problems,  and  that  have  no  further 
significance.  The  problems  of  nature  arise  when  some 
particular  individual,  impelled  by  motives  and  feelings 
of  his  own,  undertakes  to  accomplish  some  specific  thing 
in  the  perfectly  definite  situation  in  which  he  finds  him- 


1 84  THE  TEACHING  OF  PHYSICS 

self  at  the  moment  placed.  The  discipline  that  he  gets 
in  solving  the  problem  comes  from  his  own  motivated 
efforts  to  master  the  difficulties  which  obstruct  his  path, 
but  which  are  integral  parts  of  the  situation  as  a  whole. 
Hence  discipline  and  the  training  that  results  from  It 
are  not  vague  and  general  processes,  but  specific  and 
definite  results  of  the  interactions  of  the  specific  elements 
of  specific  situations. 

72.  Specific  Discipline  sometimes  Transferable.  — 
But,  notwithstanding  the  fact  that  each  particular  situa- 
tion gives  each  particular  individual  a  specific  piece  of 
discipline,  which  may  be  different  for  different  individ- 
uals in  apparently  identical  situations,  the  element  of 
discipline  derived  by  an  individual  from  one  situation 
may  enable  him  more  easily  to  master  difficulties  in  ap- 
parently dissimilar  situations.  In  other  words,  the  dis- 
cipline received  by  an  individual  in  one  situation  may 
be  "  transferred  "  and  become  manifest  in  his  reaction  to 
quite  different  situations.  The  old  doctrine  of  formal 
discipline  assumed  that  this  was  universally  true,  — 
that  the  discipline  secured  from  a  study  of  mathematics, 
for  example,  would  make  any  one  a  keen  reasoner  in  any 
other  field.  The  new  theory  states  that  this  is  true  only 
in  a  limited  way,  and  seeks  to  explain  the  limitations 
by  assuming  that  discipline  secured  by  an  individual  in 
one  situation  gives  him  increased  control  over  some  other 


THE  DISCIPLINE  OF  PHYSICS  185 

situation  only  when  the  two  situations  have  elements  in 
common,  or  "  identical  elements,"  as  Thorndike  calls 
them. 

73.  Identical  Elements.  —  The  new  theory  attempts  to 
determine  what  are  the  identical  or  common  elements  in 
any  two  situations.  But  this  is  no  easy  task,  because  of 
the  complexity  of  every  situation.  Thus  an  instructor  in 
physics  presents  an  experiment  to  his  class.  The  com- 
mon presence  of  the  class  in  one  room  watching  the  ex- 
periment would,  at  first  sight,  lead  one  to  suppose  that 
the  elements  of  experience  derived  by  each  pupil  would 
be  the  same.  But  this  is  by  no  means  necessarily  the 
case,  because  of  the  individual  differences  of  the  pupils. 
For  example,  the  common  elements  in  an  exhibition  of  a 
steam  engine  and  the  experiences  of  to-morrow  will  be 
very  different  for  boys  and  for  girls.  So  the  common 
elements  between  an  experience  in  physics  and  one  in 
the  world  at  large  are  not  confined  to  identity  of  subject 
matter.  They  may  be  psychological,  emotional,  or 
ideal;  it  is  therefore  difficult  to  locate  them  with  any 
degree  of  certainty. 

Nevertheless,  the  theory  of  identical  elements  is  sug- 
gestive of  many  fruitful  ideas  to  any  teacher  who  is 
seriously  trying  to  teach  his  science  in  such  a  way  as  to 
make  the  training  given  of  the  widest  possible  use,  i.e. 
to  give  to  its  discipline  the  largest  amount  of  transferable 


l86  THE  TEACHING  OF  PHYSICS 

value.  Some  of  these  ideas  are  here  presented  in  the 
hope  that  teachers  may  be  willing  to  try  experiments  for 
the  purpose  of  finding  out  what  common  elements  are 
most  efficient  in  securing  transferable  training ;  for  it  is 
clear  that  these  elements  will  not  be  discovered  by  Pla- 
tonic thought  or  by  any  other  a  priori  method  of  attack. 
For  purposes  of  presentation  we  shall  consider  some  of 
the  possible  common  elements :  (i)  in  subject  matter ;  (2) 
in  method  of  treatment ;  and  (3)  in  emotional  reaction. 
74.  Subject  Matter.  — The  number  of  possible  ele- 
ments of  subject  matter  which  physics  has  in  common 
with  other  situations  in  life  is  very  great.  The  phe- 
nomena of  physics  crowd  upon  every  individual  at  every 
turn  of  his  daily  experiences.  The  home,  the  street,  the 
school,  are  all  filled  to  overflowing  with  them.  The 
industries  of  the  town  and  the  country  are  rich  mines  of 
possible  elements  common  to  physics  and  the  daily  life. 
For  example,  if  the  topic  is  heat,  there  are  cook  stoves, 
furnaces,  fireless  cookers,  refrigerators,  houses,  clothes, 
frost,  dew,  drying,  sunshine,  smelting,  forging,  casting, 
besides  the  problems  connected  with  heat  engines,  gas 
manufacture,  control  of  heating  plants,  heat  equivalents 
of  coal,  matches,  sparkers,  fireworks,  firearms,  putting 
out  fires,  fire  proofing,  and  the  like.  The  teacher  who 
begins  his  work  in  heat  with  topics  of  this  sort,  carefully 
selected  with  reference  to  the  things  most  familiar  in  his 


THE  DISCIPLINE  OF  PHYSICS  187 

environment,  will  be  almost  sure  to  strike  something 
that  has  for  everybody  common  elements  of  subject 
matter. 

Thus  the  first  suggestion  from  the  theory  of  common 
elements  is  that  the  teacher  will  be  more  likely  to  give  a 
discipline  that  will  be  of  value  outside  the  physics  classes, 
if  he  makes  copious  use,  especially  at  the  beginning  of 
each  topic,  of  the  materials  ready  to  hand  in  the  im- 
mediate environment  of  the  pupils.  He  is  all  the  more 
justified  in  doing  this  (i)  because,  as  was  shown  in  Chap- 
ter V,  physics  is  the  son  of  industry ;  and  (2)  because,  as 
was  shown  in  Chapter  VII,  the  idea  which  supplies  the 
common  denominator  in  terms  of  which  the  phenomena 
of  physics  are  measured  —  that  of  energy  —  is  the 
same  idea  that  furnishes  the  common  denominator  for 
the  settlement  of  the  industrial  and  commercial  accounts 
of  the  world. 

75.  Common  Elements  of  Method.  —  The  elements  of 
method  common  to  physics  and  the  daily  life  are  also 
numerous  and  far  reaching.  As  Dewey 1  has  shown, 
"  there  is  no  difference  of  kind  between  the  methods  of 
science  and  those  of  the  plain  man.  The  difference  is 
the  greater  control  in  science  of  the  statement  of  the 
problem,  and  of  the  selection  and  use  of  relevant  ma- 

1  Dewey,  Studies  in  Logical  Theory,  p.  9  (University  of  Chicago  Press, 
1903). 


1 88  THE  TEACHING  OF  PHYSICS 

terial,  both  sensible  and  ideational.  The  two  are  related 
to  each  other  just  as  the  hit-or-miss,  trial-and-error  in- 
ventions of  uncivilized  man  stand  to  the  deliberately  and 
consecutively  persistent  efforts  of  a  modern  inventor  to 
produce  a  certain  complicated  device  for  doing  a  com- 
prehensive piece  of  work.  Neither  the  plain  man  nor  the 
scientific  inquirer  is  aware,  as  he  engages  in  his  reflective 
activity,  of  any  transition  from  one  sphere  of  existence 
to  another.  .  .  .  Observation  passes  into  development  of 
hypothesis ;  deductive  methods  pass  to  use  in  descrip- 
tion of  the  particular ;  inference  passes  into  action  with 
no  sense  of  difficulty  save  those  found  in  the  particular 
task  in  question.  The  fundamental  assumption  is  con- 
tinuity in  and  of  experience."  l 

But  if  the  scientific  method  of  solving  problems  does 
not  differ  in  kind  from  that  of  the  plain  man,  the  two  do 
differ  in  the  degree  of  refinement  to  which  the  various 
phases  of  thinking  are  pushed.  Herein  lies  one  of  the 
great  opportunities  for  the  physics  teacher.  He  has  the 
chance  to  help  refine  and  sublimate  the  thinking  of  the 
plain  man  until  it  becomes  scientific.  And  if  the  pupils 
begin  their  thinking  about  physics  in  the  method  to  which 
they  are  accustomed,  namely,  that  of  the  plain  man, 
and  are  led  on  to  more  and  more  critical  and  impersonal 

1  Cf.  also  Minot,  The  Method  of  Science,  Science,  Vol.  xxxiii,  p.  119, 
Jan.  27,  1911. 


THE  DISCIPLINE  OF  PHYSICS  189 

habits  of  thought,  does  not  this  tend  to  preserve  common 
elements  of  method?  And  the  more  these  common  ele- 
ments are  preserved,  the  greater  is  the  transferable  value 
of  the  teaching. 

The  methods  of  teaching  now  in  use  generally  fail  to 
do  this,  as  shown  in  Chapter  IV.  When  the  student 
enters  upon  his  study  of  physics,  he  strikes  at  the  very 
beginning  impossible  definitions  and  mathematical  state- 
ments of  laws  which  are  as  intelligible  to  him  as  if  they 
were  written  in  Chinese  characters.  He  discovers  no 
elements  common  to  physics  and  the  rest  of  his  experi- 
ences, and  is  immediately  and  irretrievably  cut  off  from 
securing  from  his  study  of  physics  a  discipline  that  shall 
be  of  any  great  value  to  him  outside  of  the  physics 
classes.  Hence,  those  teachers  who  would  give  trans- 
ferable training  in  physics  should  reason  like  plain  men 
at  the  beginning.  The  upper  limit  to  their  reasoning  is 
set  only  by  their  own  abilities  and  those  of  their  pupils. 

76.  Ideals  of  Method.  — Besides  the  common  elements, 
there  is  another  factor  which  is  of  great  importance  in 
making  a  method  transferable.  After  a  very  illuminating 
discussion  of  this  topic,  this  factor  is  thus  described  by 
Bagley : l  "  What  I  carry  over  from  my  school  work  to 
my  farm  work  is  not  a  generalized  habit  of  work,  but  a 
generalized  ideal  of  work.  This  ideal  furnishes  a  motive 

1  Bagley,  The  Educative  Process,  p.  212"^ (New  York,  Macmillan,  1910). 


190  THE  TEACHING  OF  PHYSICS 

and  this  motive  holds  me  to  conscious  persistent  effort 
until  the  new  habit  has  become  effective,  until  the  dis- 
tracting influences  no  longer  solicit  passive  attention. 
//  I  had  acquired  a  specific  habit  of  work  in  one  field 
without  at  the  same  time  acquiring  a  general  ideal  of  work, 
my  acquisition  of  a  specific  habit  in  another  field  would 
probably  not  be  materially  benefited.11  Again,  page  216 : 
"  This  increased  power  must  always  take  the  form  of  an 
ideal  that  will  function  as  a  judgment  and  not  of  an  un- 
conscious predisposition  that  will  function  as  habit.  In 
other  words,  unless  the  ideal  has  been  developed  con- 
sciously, there  can  be  no  certainty  that  the  power  will 
be  increased,  no  matter  how  intrinsically  well  the  sub- 
ject has  been  mastered." 

In  further  definition  of  the  point  Bagley  continues, 
p.  222  :  "  An  ideal  is  a  type  of  condensed  experience. 
It  is  the  upshot  of  a  multitude  of  reactions  and  adjust- 
ments, both  individual  and  racial.  As  a  condensed  ex- 
perience, it  functions  in  the  process  of  judgment.  It 
serves  as  a  conscious  guide  to  conduct,  especially  in 
novel  and  critical  relations.  .  .  .  The  development  of  an 
ideal  is  both  an  emotional  and  an  intellectual  process,  but 
the  emotional  element  is  by  far  the  more  important.  Ideals 
that  lack  the  emotional  coloring  are  simply  intellectual 
propositions  and  have  little  directive  force  upon  conduct. 
.  That  the  emotional  element  is  dominant  in  the  de- 


THE  DISCIPLINE  OF  PHYSICS  191 

velopment  of  ideals  indicates  that  mere  didactic  instruc- 
tion from  the  intellectual  standpoint  is  not  sufficient. 
The  emotional  spirit  of  the  instruction  is  the  factor  that 
counts." 

Since  a  scientific  habit  of  mind,  when  developed  in 
physics,  is  not  transferable,  while  a  conscious  ideal  of 
scientific  method  is  transferable,  it  is  important  to  note 
the  distinction  between  a  habit  and  an  ideal.  Among 
the  ideals  which  physics  may  well  foster  are  those  of  sus- 
pended judgment,  of  open-mindedness,  of  just  weighing 
of  evidence,  of  impartial  observation,  of  impersonal  judg- 
ment, of  trying  to  get  at  all  the  facts.  These  ideals  are 
the  ones  which  a  teacher  who  desires  to  give  transferable 
training  in  physics  will  endeavor  to  develop  consciously 
in  his  students.  And  can  physics  retain  its  hold  on 
general  education,  if  it  is  unable  to  do  its  share  toward 
building  up  such  general  ideals  as  these? 

77.  The  Emotional  Element.  —  But  Bagley  has 
pointed  out  that  in  an  ideal  the  emotional  element  is  by 
far  the  most  important.  This  emotional  factor  is  the 
third  of  the  categories  under  which  we  are  seeking  the 
elements  common  to  physics  and  the  rest  of  the  world. 
In  this  field  it  is  at  once  clear  that  physics  and  the  world 
at  large  have  all  possible  emotions  in  common.  The 
feelings  evoked  by  instruction  in  physics  range  all  the 
way  from  exultant  enthusiasm  and  self-forgetful  devo- 


192  THE  TEACHING  OF  PHYSICS 

tion,  to  melancholy  despondency,  anger,  and  despair. 
It  is  because  of  this  wide  range  of  possible  emotions  that 
another  great  opportunity  is  open  to  the  teacher  in  select- 
ing and  emphasizing  those  emotions  that  are  of  the  high- 
est order  and  of  the  greatest  value  both  to  the  individual 
and  to  society.  It  is  in  doing  this  that  the  teacher  shows 
his  most  subtle  art,  since  the  work  must  be  done  un- 
consciously. A  conscious  exhortation  to  enjoy  any  given 
emotion  ends  disastrously.  Feelings  seem  to  be  con- 
trolled by  the  situation  as  a  whole. 

78.  The  Intellectual  Feeling  of  Wonder.— In  Chapter 
V  it  has  been  pointed  out  that  there  is  one  feeling  that  is 
particularly  characteristic  of  true  science,  namely,  wonder, 
which  is  the  "  originator  and  continuer  of  science."  If 
the  teacher  would  cultivate  this  feeling  in  his  pupils, 
he  must  know  himself  how  it  feels,  and  must  be  able  to 
detect  its  presence  in  his  pupils.  He  must,  therefore, 
know  some  of  its  characteristics.  This  intellectual 
feeling  of  wonder  is  thus  described  by  Dewey : 1  "In- 
tellectual feeling,  like  all  feeling,  takes  the  form  of  an 
interest  in  objects.  It  is  directed  outward;  it  can  find 
its  satisfaction  only  in  an  outgoing  activity  of  self.  In- 
tellectual feeling  considered  in  this  aspect  is  wonder. 
Wonder  is  the  attitude  which  the  emotional  nature  spon- 
taneously assumes  in  front  of  a  world  of  objects.  The 
1  Dewey,  Psychology,  pp.  303  sq.  (New  York,  Harpers,  1897). 


THE  DISCIPLINE  OF  PHYSICS  193 

feeling  is  utterly  incomprehensible  as  a  purely  personal 
or  selfish  feeling.  Wonder  is  the  first  and  final  expression 
of  the  individual  as  it  finds  a  universe  over  against  it.  ... 
Wonder  is  the  simple  recognition  that  objects  have  sig- 
nificance for  us  beyond  the  mere  fact  of  their  existence. 
A  wide  development  of  the  feeling  of  wonder  constitutes 
disinterestedness,  the  primary  requisite  for  all  investiga- 
tion. .  .  .  Wonder  necessarily  requires  the  devotion 
of  one's  self  to  the  object  wholly  for  the  sake  of  the  latter. 
...  It  is  vitiated  by  the  presence  of  any  merely  per- 
sonal interest.  When  the  activity  occurs  not  for  the  sake 
of  the  object,  but  for  the  sake  of  satisfying  the  personal 
emotion  of  wonder,  we  have,  not  disinterestedness,  but 
curiosity.  Curiosity  is  an  abnormal  feeling.  It  is  pos- 
sible, however,  for  intellectual  feelings  to  assume  still 
more  unhealthy  forms.  Such  we  have  when  knowledge 
is  sought  for  the  gratification  of  vanity,  or  for  the  sake 
of  show  or  power.  A  more  subtle  form  is  that  distinc- 
tively nineteenth-century  disease,  the  love  of  culture,  as 
such.  .  .  .  Culture  of  our  mental  powers  is  made  an 
end  in  itself,  and  knowledge  of  the  universe  of  objects  is 
subordinated  to  this.  .  .  .  Here,  as  in  all  such  cases, 
the  attempt  defeats  itself.  The  only  way  to  develop 
self  is  to  make  it  become  objective;  the  only  way  to 
accomplish  this  is  to  surrender  the  interests  of  the 
personal  self.  Self  culture  reverses  the  process,  and 


IQ4  THE  TEACHING  OF  PHYSICS 

attempts  to  employ  self-objectification  or  knowledge  as 
a  mere  means  to  the  satisfaction  of  these  personal  inter- 
ests. The  result  is  that  the  individual  never  truly  gets 
outside  of  himself." 

These  being  the  chief  characteristics  of  the  emotion 
of  wonder,  it  is  easy  for  the  teacher  to  know  whether 
this  feeling  is  at  work  among  his  pupils.  If  they  lose 
themselves  in  the  objective  things  they  are  doing  and 
become  absorbed  in  the  study  of  the  problem  as  an  ob- 
jective thing,  the  chances  are  very  great  that  their  emo- 
tions are  of  the  right  sort.  This  absorption  in  the 
objective  study  of  problems  is  a  well-recognized  mark  of 
genius,  and  a  sign  of  the  process  of  acquiring  true  knowl- 
edge. As  Henderson  puts  it : 1  "  In  signaling  out 
knowledge  as  the  one  cardinal  virtue,  one  does  not  mean 
an  idle  erudition,  a  mass  of  abstract  information,  a  tech- 
nical equipment  for  the  sake  of  the  loaves  and  the  fishes, 
an  acquaintance  with  one  or  more  foreign  languages 
without  anything  special  to  say  in  any  one  of  them ;  but 
one  means  that  cosmic  attitude  of  mind  which  leads  one  to 
seek  to  know  things  as  they  are,  and  to  make  one's  thought 
and  action  partake  of  the  same  soundness  and  reality." 

79.   True  Discipline  Requires  Motivation.  —  Perhaps 
the  reader  is  wondering  what  all  this  has  to  do  with  dis- 
cipline.    The  connection  comes  from  the  fact  that  this 
1  C.  H.  Henderson,  Children  of  Good  Fortune,  p.  195. 


THE  DISCIPLINE  OF  PHYSICS  195 

emotion  of  wonder  manifests  itself  in  an  interest  in  ob- 
jects for  the  sake  of  the  objects.  "  Because  interests  are 
things  that  have  to  be  worked  out  in  life  and  not  merely 
indulged  in  themselves,  there  is  plenty  of  room  for  dif- 
ficulties and  obstacles  which  have  to  be  overcome,  and 
whose  overcoming  forms  '  will '  and  develops  the  flexible 
and  firm  fiber  of  character.  To  realize  an  interest  means 
to  do  something,  and  in  the  doing  resistance  is  met  and 
must  be  faced.  Only  difficulties  are  now  intrinsic ;  they 
are  significant;  their  meaning  is  appreciated  because 
they  are  felt  in  their  relation  to  the  impulse  or  habit  to 
whose  outworking  they  are  relevant.  Moreover,  for 
this  reason,  there  is  motive  to  gird  up  one's  self  to  meet 
and  persistently  to  deal  with  the  difficulties,  instead  of 
getting  discouraged  at  once,  or  having  to  resort  to 
extraneous  motives  of  hope  and  fear  —  motives  which, 
because  external,  do  not  train  '  will '  but  only  lead  to 
dependence  upon  others.  .  .  .  There  is  only  discipline 
when  one  can  put  one's  powers  economically,  freely,  and 
fully  at  work  upon  work  that  is  intrinsically  worth  doing." 1 
For  this  reason,  the  problem  of  securing  the  best  dis- 
cipline is  the  problem  of  securing  the  best  motivation  for 
the  work.  But  the  best  motivation  comes  from  the  emo- 
tion of  wonder,  which  is  the  spontaneous  feeling  ojL  the 

1  Dewey,  Interest  as  Related  to  Will,  p.  32  (University  of  Chicago  Press, 
1903)- 


ig6  THE  TEACHING  OF  PHYSICS 

self  before  a  world  of  objects,  and  which  manifests  itself 
in  an  impersonal  and  unselfish  effort  to  get  at  the  real 
facts  of  the  case. 

This  chapter  contains  the  statement  of  what  may  be 
called  the  working  hypotheses  of  the  coming  democratic 
education  as  they  apply  to  physics.  They  are  not  fin- 
ished laws  and  final  truths ;  for  such  are  found  only  in 
Platonic  thought  and  its  doctrine  of  formal  discipline. 
What  is  most  needed  at  present  is  intelligent  experimen- 
tation to  test  the  validity  of  these  working  hypotheses 
and  to  correct  and  amplify  them  as  may  be  found  ex- 
pedient. The  problem,  which  they  define  is  a  relatively 
new  one  in  education,  and  may  be  stated  thus :  to  find 
what  and  how  many  of  the  elements  that  are  common  to 
physics  and  to  life  can  be  used  to  give  a  discipline  which 
shall  be  most  efficient  in  developing  the  characters  of 
the  majority  of  the  pupils  and  which  shall  also  have  the 
greatest  possible  transferable  value. 

SUPPLEMENTARY  READING 

HECK,  W.  H.    Mental  Discipline  and  Educational  Values.    2d  ed. 

New  York,  Lane,  1911. 
Contains  a  summary  of  results  of  others  and  a  good  bibliography. 

BAGLEY,  W.  C.   The  Educative  Process,  Chapters  XIII-XV.   New 
York,  Macmillan,  1910. 

Educational  Values,  Chapters  VII-XII.     New  York,  Mac- 
millan, 1911. 


THE  DISCIPLINE  OF  PHYSICS  197 

DEWEY,  JOHN.     The  School  and  Society.    University  of  Chicago, 
Press,  1900. 

Moral  Principles  in  Education.    Boston,  Houghton  Mifflin, 

1909. 

Psychology,  Chapters  XIV,  XXII.   New  York,  Harper,  1897. 

Interest  as  Related  to  Will.    University  of  Chicago  Press, 

1903. 

BENNETT,  C.  J.   C.     Formal  Discipline.    New  York,  Teachers 

College,  1907. 
HUGHES,  J.  L.    FroebeVs  Educational  Laws,  Chapters  i,  3,  4,  n. 

New  York,  Appleton,  1897. 
HUXLEY,  T.  H.    Essays  on  Science  and  Education,  Nos.  4,  6  7,  8. 

New  York,  Appleton,  1904. 
JUDD,  C.  H.    Genetic  Psychology  for  Teachers,  Chapters  1-5.    New 

York,  Appleton,  1909. 

DOPP,  KATHERINE  E.     The  Place  of  Industries  in  Elementary  Edu- 
cation.   University  of  Chicago  Press,  1907. 
LANKESTER,  R.    The  Kingdom  of  Man,  Chapter  I.    New  York, 

Holt,  1907. 
OSTWALD,    W.    Wider    der    Schulelend;     ein    Notruf.    Leipzig, 

Akademische  Verlagsgeselschaft,  1909. 
LAISANT,  C.  A.    L  Education  fond&e  sur  la  Science.    Paris,  Alcan, 

1905. 


PART  III 
HINTS  AT  PRACTICAL  APPLICATIONS 

CHAPTER  IX 

THE  CONCRETE  PROBLEM 

80'.  Importance  of  Daily  Experiences.  —  In  the  pre- 
ceding chapter,  emphasis  has  been  laid  on  the  idea  that 
instruction  should  begin  with  discussions  of  experiences 
of  the  daily  life  and  with  practical  applications  of  physics. 
The  claim  was  made  that  this  sort  of  an  approach  was 
much  more  likely  to  supply  the  kind  of  motivation  that 
is  needed  if  the  study  of  physics  is  to  give  real  discipline. 
This  idea  is  entirely  in  harmony  with  the  conclusion  in 
Chapter  V  that  physics  is  the  son  of  industry,  and  with 
the  findings  of  Chapter  VI  that  the  method  of  science 
begins  with  a  problem  defined  by  a  human  need,  and 
with  the  facts  presented  in  Chapter  VII  showing  the 
present  close  relationship  of  physics  and  industry,  due  to 
their  common  practice  of  evaluation  in  terms  of  energy. 

Notwithstanding  this  unanimity  in  pointing  to  daily 
experiences  and  industry  as  the  best  starting  point  for 
instruction,  no  one  should  conclude  that  the  study  of 

198 


THE  CONCRETE  PROBLEM  199 

physics  should  remain  entirely  in  this  domain  of  the 
practical.  As  has  been  noted  on  page  189,  the  upper 
limit  of  the  teaching  is  placed  only  by  the  abilities  of  the 
teacher  and  the  pupils.  That  a  free  use  of  industrial 
materials  and  practical  applications  at  the  beginning  need 
not  and  should  not  make  the  study  basely  utilitarian 
has  been  pointed  out  also  by  Bagley  as  follows : 1  — 

"  It  is  much  more  probable  that  the  emphasis  of  eco- 
nomic applications  will  make  a  much  more  forcible  and 
much  more  general  appeal,  and  thus  serve  more  effec- 
tively to  give  point  and  vitality  to  the  ideas  of  method 
and  procedure  and  thus  turn  them  into  ideals.  After 
all,  the  prime  source  of  emotional  factors  is  the  funda- 
mental needs  of  the  individual,  and  the  next  most  pro- 
lific source  is  humanity  and  its  needs.  When  a  high 
school  pupil  finds  that  a  rigidly  controlled  method  of 
procedure,  coupled  with  a  rigorous  exclusion  of  irrelevant 
factors,  including  his  own  prejudice  and  bias,  gains  re- 
sults that  are  of  service  to  him  and  to  the  race,  it  is  likely 
that  he  will  have  much  more  effective  respect  for  the 
method  and  its  rigorous  qualities  than  he  would  gain  if 
it  were  attempted  to  carry  him  through  a  series  of  ex- 
periences ending  in  the  contemplation  of  a  logical  and 
coherent  body  of  facts  and  principles." 

"  At  every  point,  the  advocate  of  applied  science  seems 
1  Bagley,  Educational  Values,  pp.  207  sq.  (New  York,  Macmillan,  1911). 


200  THE  TEACHING  OF  PHYSICS 

to  have  the  better  of  the  argument,  —  so  long  as  he 
limits  his  plea  to  the  approach,  and  so  long  as  he  recog- 
nizes the  immanence  of  the  method  and  spirit  of  science, 
as  compared  with  its  facts  and  principles.  He  may  well 
maintain  that  the  method  and  spirit  have  no  meaning, 
except  as  productive  of  facts  and  principles,  and  that  if 
such  facts  and  principles  can  be  so  chosen  as  to  represent 
a  maximum  of  utility  without  at  the  same  time  inter- 
fering with  the  fulfillment  of  the  disciplinary  functions, 
it  is  economy  to  make  the  choice  on  this  basis." 

81.  Industrial  Study  of  Science.  —  It  will  be  noted 
that  the  point  of  view  here  presented  as  applied  to  phys- 
ics is  one  of  importance  for  industrial  education  as  well. 
That  many,  if  not  all,  of  the  attempts  at  industrial  edu- 
cation have  been  decried  by  the  formal  disciplinarians 
as  wholly  utilitarian  and,  therefore,  educationally  use- 
less, is  due,  first,  to  the  fact  that  this  is  sometimes  true ; 
and  second,  to  the  fact  that  few  realize  that  for  young 
students  a  richer  discipline  can  be  given  by  a  training 
that  is  founded  on  the  industries,  but  flies  higher,  than 
by  one  that  flies  too  high  at  the  start.  Even  the  eagle 
has  to  come  to  earth  now  and  then  for  real  nourishment. 
There  is  nothing  inherently  incompatible  between  in- 
dustrial education  and  the  discipline  of  pure  science. 
In  fact,  from  the  point  of  view  here  presented,  they  are 
identical ;  and  the  clergyman,  the  doctor,  and  the  lawyer 


THE   CONCRETE   PROBLEM  2OI 

need  this  mental  discipline  founded  on  industry  even 
more  than  do  the  toilers  with  their  hands.  It  is  one  of 
the  most  basic  factors  of  any  genuine  liberal  culture. 

For  this  reason  the  discovery  of  the  methods  of  render- 
ing this  industrial  study  of  science,  or  this  scientific  study 
of  industry,  if  you  prefer,  an  effective  weapon  of  genuine 
educational  discipline,  is  at  least  as  important  for  the 
academically  standardized  schools  and  colleges  of  liberal 
culture  as  it  is  for  the  industrial  schools.  It  is  a  conscious 
ideal  of  scientific  procedure  that  is  the  goal,  and  "  the 
future  of  our  civilization  depends  upon  the  widening 
spread  and  deepening  hold  of  the  scientific  habit  of  mind ; 
and  the  problem  of  problems  in  our  education  is  there- 
fore to  discover  how  to  mature  and  make  effective  this 
scientific  habit.  Mankind  so  far  has  been  ruled  by 
things  and  by  words,  not  by  thought;  for  till  the  last 
few  moments  of  history,  humanity  has  not  been  in  pos- 
session of  the  conditions  of  pure  and  effective  thinking. 
Without  ignoring  in  the  least  the  consolation  that  has 
come  to  men  from  their  literary  education,  I  would  even 
go  so  far  as  to  say  that  only  the  gradual  replacing  of  a 
literary  by  a  scientific  education  can  assure  to  man  the 
progressive  amelioration  of  his  lot.  Unless  we  master 
things,  we  shall  continue  to  be  mastered  by  them ;  the 
magic  that  words  cast  upon  things  may  indeed  disguise 
our  subjection  or  render  us  less  dissatisfied  with  it,  but 


202  THE  TEACHING  OF  PHYSICS 

after  all  science,  not  words,  casts  the  only  compelling 
spell  upon  things."1 

82.  The  Administrative  System.  —  In  the  light  of  the 
facts  and  working  hypotheses  presented  in  the  preceding 
pages,  it  is  clear  that  the  general  problem  of  the  physics 
teacher  is  that  of  finding  out  how  to  make  the  work  in 
physics  contribute  most  effectively  to  the  development 
among  the  pupils  of  transferable  ideals  of  scientific 
method.  It  is  equally  clear  that  the  methods  that  have 
been  used  to  develop  physics  teaching  into  its  present 
well-organized  condition  are  utterly  incapable  of  yield- 
ing the  desired  result.  These  methods  have  been  de- 
scribed in  Chapters  I  and  III,  and  consist  in  the  setting 
up  of  a  syllabus  of  topics  and  experiments  sanctioned  by 
the  "  authority  of  official  utterance,"  and  enforced  by 
college  entrance  examinations.  The  conscious  purpose 
of  it  all  is  that  the  student  may  secure  "  a  comprehensive 
and  connected  view  of  the  most  important  facts  and  laws 
of  elementary  physics."2 

This  system  of  standardization  of  schools  and  courses 
has  been  very  effective  as  far  as  solving  the  problems  of 
school  administration  is  concerned.  By  the  unit  system 
which  has  been  developed  any  college  can  compute  the 

1  Dewey,  Science  as  Subject  Matter  and  as  Method,  Science,  Vol.  31, 
p.  127,  Jan.  28,  1910. 
9  Ante,  p.  61. 


THE  CONCRETE  PROBLEM  203 

fitness  of  a  boy  to  enter  college  with  a  probable  error  of 
perhaps  twenty  school  minutes ;  and  the  Carnegie  Foun- 
dation can  determine  the  fitness  of  a  college  to  have  its 
venerable  professors  pensioned  with  a  probable  error  of 
one  semester-hour.  All  this  is  excellent,  and  an  admi- 
rable thing  for  administrative  convenience.  By  it  the 
administration  of  the  schools  has  been  reduced  to  an 
exact  science.  It  has  brought  order  out  of  chaos,  has 
developed  a  system  of  absolute  units  in  terms  of  which 
all  school  phenomena  may  be  measured,  and  has  estab- 
lished a  "  credit  system  "  which  makes  it  possible  for  a 
student  to  get  a  degree  without  thinking  for  it.  It  has 
led  to  the  belief,  current  in  many  quarters,  that  all  edu- 
cational problems  are  at  bottom  financial  problems. 
On  the  other  hand,  it  has  tried  to  force  uniformity  of 
practice  where  such  uniformity  was  impossible,  thereby 
killing  the  thing  for  which  alone  administration  exists. 
83.  The  Needs  of  the  Masses.  —  Excellent  and  im- 
portant as  this  administrative  progress  of  the  schools 
has  been,  it  has  left  the  educational  problem  practically 
where  it  was  when  the  high  schools  were  founded.  As 
has  been  noted  (ante,  p.  12),  the  high  schools  were  es- 
tablished in  response  to  a  demand  from  the  masses  of  the 
people  for  a  general  education  suited  to  their  needs.  No 
one  can  read  the  daily  papers  to-day,  not  to  mention  the 
literature  of  education,  without  seeing  clearly  that  the 


204  THE  TEACHING  OF  PHYSICS 

masses  of  the  people  are  making  the  same  demands  at 
the  present  time.  And  the  reason  for  this  is  not  hard  to 
find,  as  has  been  pointed  out  by  Thorndike  (ante,  p.  181), 
"  The  American  public  school  system  rests  on  a  total 
disregard  of  hereditary  mental  differences  between  the 
classes  and  the  masses."  One  curriculum,  consisting  of 
so  many  bundles  of  ready-made  information,  selected 
by  a  Platonic  ideal  of  the  immutable  nature  of  children's 
minds,  was  made  to  do  duty  for  everybody. 

The  one  curriculum  has  now  broken  down  to  make  way 
for  the  many ;  but  still  the  many  fail  to  reach  the  masses. 
The  schooling  they  offer  is  not  democratic,  notwith- 
standing the  fact  that  rich  and  poor  mingle  together  on 
equal  terms  in  the  classes.  And  no  wonder,  for  "  the 
doctrine  of  democracy  in  education  and  the  doctrine  of 
formal  discipline  cannot  well  be  harmonized." 1  An 
aristocracy  may  succeed  in  divorcing  thinking  from  the 
other  functions  of  life,  but  every  member  of  a  democracy 
must  feel  and  act,  as  well  as  think. 

84.  Syllabi  do  not  Solve  the  Problem.  —  Not  only 
is  the  system  of  regulating  physics  courses  by  syllabi 
and  externally  applied  examinations  wholly  incompatible 
with  a  democratic  or  industrial  study  of  physics,  but 
also  the  methods  of  presentation  which  that  system  has 
called  into  being  cannot  be  reconciled  with  the  working 

1  Heck,  Menial  Discipline,  26.  ed.,  p.  125. 


THE   CONCRETE   PROBLEM  205 

hypotheses  of  this  newer  education.  As  shown  in  Chap- 
ter IV,  these  methods  seek  to  impose  a  system  of  ready- 
made  information  on  the  pupil  by  the  adult  method 
of  text  — discussion  — application.  In  the  laboratory 
work  the  results  of  this  system  are  often  distressing. 
Much  of  the  work  consists  of  careful  measurements  of 
known  constants.  The  success  of  the  work  is  too  often 
judged  by  the  agreement  of  the  result  with  its  absolute 
or  predetermined  value.  Since  the  apparatus  remains 
the  same  in  each  laboratory  year  after  year,  the  results 
required  soon  become  preserved  in  student  circles.  Un- 
der these  conditions  the  ideals  developed  by  the  work  are 
anything  but  those  of  scientific  method. 

From  all  this  it  appears  that  the  contents  of  Chapters 
I-IV  of  this  book,  while  essential  for  an  understanding 
of  the  present  problem,  shed  little  light  on  the  way  to 
proceed  in  the  solution  of  that  problem.  In  fact  they 
may  be  said  to  have  rather  a  negative  value  in  warning 
us  how  not  to  proceed  if  we  would  attain  results  of  value 
to  education.  They  describe  the  way  in  which  the 
schools  reached  their  present  administrative  efficiency; 
but  education  shall  not  live  by  administration  alone. 

85.  Experimentation  Needed.  —  But  if  the  problem 
cannot  be  solved  by  the  methods  previously  tried,  how 
can  it  be  done?  This  question  seems  hardly  necessary 
after  the  discussions  in  Chapters  V  to  VIII.  Whenever 


206  THE  TEACHING  OF  PHYSICS 

a  human  need  has  made  itself  felt  and  denned  a  problem, 
how  has  the  problem  been  solved,  if  not  by  the  method 
of  science?  The  only  reason  why  this  method  has  not 
been  tried  sooner  is  that  the  training  and  discipline 
which  we  science  teachers  received  did  not  relate  to 
significant  things  and  so  has  not  proved  itself  to  be 
transferable;  therefore,  few  have  thought  of  trying  to 
apply  the  methods  of  their  physics  to  the  problems  of 
education;  and  the  few  who  have  thought  of  it  have 
been  restrained  until  very  recently  by  the  excellent 
administrative  system  which  has  just  been  mentioned. 
It  is,  however,  perfectly  clear  that  if  progress  is  to  be 
made  in  teaching  physics  for  purposes  of  general  demo- 
cratic education,  opportunity  will  have  to  be  given  for 
careful  and  well-directed  experimentation.  This  means 
that  all  attempts  at  detailed  uniformity  of  subject  mat- 
ter will  have  to  be  abandoned,  and  all  detailed  syllabi 
revoked.  In  physics  the  only  kind  of  syllabus  that  will 
not  do  injury  is  the  kind  adopted  by  the  North  Central 
Association  of  Colleges  and  Secondary  Schools ;  and  this 
contains  only  eighty-one  topics,  these  being,  as  men- 
tioned on  page  67,  those  to  which  no  physics  teachers 
offer  any  objection.  This  is  enough  to  furnish  the  com- 
mon core  of  different  courses  in  physics  without  ham- 
pering the  teacher  in  adapting  the  work  to  his  particular 
community. 


THE  CONCRETE  PROBLEM          207 

86.   Problems    Needing    Experimental    Solution.  — 

Wherever  such  detailed  and  obstructive  syllabi  have 
ceased  to  intimidate  teachers  by  their  "  authority  of 
official  utterance,"  experimentation  may  well  begin. 
Such  experimentation  may  well  be  directed  at  first 
toward  settling  two  questions;  namely,  first,  what  ma- 
terials in  the  industries  and  the  daily  life  have  enough 
elements  in  common  with  principles  of  physics  to  be 
available  and  useful  in  making  the  approach  to  those 
principles?  In  other  words,  what  materials  of  common 
experience  can  be  effectively  used  in  defining  problems 
that  will  not  only  be  significant  to  the  pupils,  but  will 
also  lead  somewhere  in  physics?  And  secondly,  what 
things  in  physics  are  worthy  of  study?  Is  accelerated 
motion,  for  example,  a  topic  from  which  the  pupils  gain 
enough  transferable  discipline  to  entitle  it  to  the  time 
required  to  make  it  clear?  Or  are  there  other  topics 
which  yield  larger  returns  for  the  same  time  ?  Questions 
of  this  sort  cannot  be  answered  on  a  priori  grounds. 
The  fact  that  acceleration  is  a  fundamental  idea  in  New- 
tonian analytical  and  celestial  mechanics  is  not  in  itself 
a  warrant  for  including  it  in  the  course.  If  it  can  be 
shown  to  have  enough  elements  in  common  with  life 
outside  of  school  to  make  it  significant  to  the  pupils, 
well  and  good ;  but  if  this  is  not  the  case,  it  will  have 
to  make  way  for  more  vital  topics. 


208  THE  TEACHING  OF  PHYSICS 

Before  very  much  can  be  done  in  this  line  of  experi- 
mentation, the  number  of  topics  treated  in  most  of  the 
textbooks  will  have  to  be  lessened,  and  more  significant 
material  introduced.  All  of  the  texts  extensively  used 
at  present  have  in  the  neighborhood  of  575  numbered 
paragraphs,  each  containing,  from  the  fact  that  it  is 
numbered,  one  or  more  new  ideas.  Since  the  "  unit  " 
in  physics  is  denned  as  120  hours  of  class  work,  the 
teacher  who  uses  one  of  these  books  has  about  twelve 
and  a  half  minutes  for  each  paragraph.  In  this  time 
he  must  present  his  illustrative  material,  his  demon- 
strations, his  questions,  his  laboratory  work,  and  his 
problems.  This  condition  reduces  well-nigh  to  zero 
the  chances  for  needed  repetition,  informal  discussion, 
and  the  bringing  in  of  neighborhood  materials  by  way 
of  introduction.  It  is  useless  to  urge  the  teacher  to 
skip  paragraphs,  for  the  argument  is  usually  so  logically 
arranged  that  the  omission  of  paragraphs  renders  the 
subject  even  more  unintelligible. 

87.  Summary  of  Conclusions.  —  The  teacher  who 
has  followed  sympathetically  the  discussions  in  all  the 
preceding  chapters  may  now  give  a  more  specific  mean- 
ing to  the  slogan  of  modern  physics  teaching,  —  bring 
the  physics  close  to  the  daily  lives  of  the  pupils.  If 
the  discussions  have  not  proved  convincing,  they  must 
at  least  have  shown  that  the  content  of  this  slogan  is 


THE  CONCRETE  PROBLEM  209 

by  no  means  as  simple  as  at  first  sight  it  appears  to  be. 
This  content,  as  here  interpreted  in  the  light  of  the  new 
theories  of  democratic  education,  may  be  summarized 
somewhat  as  follows :  — 

Physics  is  the  son  of  industry  and  the  spirit  of  wonder. 
From  its  father  it  has  inherited  its  method  of  solving 
problems,  —  a  method  developed  by  Germanic  races 
and  quite  distinct  from  that  of!  Platonic  thought.  From 
its  mother  it  has  inherited  that  impersonal  and  unself- 
ish disinterestedness  which  makes  it  open-minded  and 
ever  ready  to  accept  the  most  expedient  and  general 
solution  of  a  problem  as  the  truth. 

The  most  important  individual  characteristic  of  the 
child  Physics  is  his  interpretation  of  the  causal  principle 
as  meaning  that  every  natural  phenomenon  is  related  to 
some  others ;  so  that  no  one  object  ever  moves  or  changes 
unless  some  other  object  or  objects  are  simultaneously 
affected  in  some  way.  To  physics  every  act  produces  its 
indelible  effect  on  the  cosmos,  however  slight  that  effect 
may  be.  Impelled  by  this  deep-seated  intuition  of  the 
universal  relativity  of  phenomena,  physics  has  spent  its 
life  endeavoring  to  give  concrete  expression  to  the  intui- 
tion and  to  reduce  it  to  the  realms  of  quantitative, 
mathematical  form  and  logic.  It  has  done  this  by  seek- 
ing the  related  factors  in  phenomena  and  by  determin- 
ing by  measurement  the  mathematical  form  that  most 


210  THE  TEACHING  OF  PHYSICS 

nearly  expresses  the  relationship.  In  this  it  has  been 
eminently  successful,  for  its  comprehensive  principle  of 
the  conservation  of  energy  may  be  regarded  as  a  quanti- 
tative and  logical  statement  of  the  fact  that  no  single 
physical  quantity  ever  changes  its  value  or  varies,  unless 
some  related  quantity  changes  its  value  or  varies  in  a 
corresponding  way. 

In  its  long  search  for  the  related  elements  of  phenom- 
ena, and  for  the  constant  forms  that  express  that  in- 
terdependence, physics  has  finally  chosen  as  the  most 
expedient  forms  for  expressing  the  most  general  rela- 
tionships among  terrestrial  phenomena  those  that  ex- 
press energy  relations.  In  this  he  again  shows  his  close 
kinship  with  industry;  since  energy  is  the  factor  in 
terms  of  which  industrial  and  commercial  relationships 
are  ultimately  determined. 

Thus  physics  consists  of  two  fundamental  elements, 
namely,  (i)  that  activity  which,  inspired  by  the  spirit 
of  wonder,  takes  from  the  industries  their  method  of 
solving  problems,  perfects  it,  and  applies  it  to  the  solu- 
tion of  the  problems  of  finding  the  constant  relations 
that  exist  among  the  varying  elements  of  the  flux  of 
phenomena;  and  (2)  the  knowledge  which  results  from 
this  activity,  and  which  is  always  valid  within  the  limits 
set  by  the  accuracy  of  the  experimental  data.  When- 
ever physics  is  used  for  purposes  of  general  education, 


THE  CONCRETE  PROBLEM          211 

both  of  these  elements  must  be  prominent.  At  present 
the  second  and  less  important  receives  almost  all  of  the 
attention  of  both  teacher  and  pupil. 

88.  Bringing  Physics  close  to  the  Daily  Life.  — 
When  considering  how!"  to  bring  physics  as  thus  defined 
close  to  the  daily  life  of  the  pupil,  we  must  first  remember 
Dewey's  remark  that  "  education  is  not  preparation 
for  life,  it  is  life."  Hitherto  physics  teaching  has  gen- 
erally been  conducted  as  preparation  for  the  career  of 
a  physicist.  Even  if  we  grant  that  the  present  methods 
are  well  devised  to  secure  that  end,  the  end  itself  is 
absurd.  In  1910,  there  were  167,000  pupils  studying 
physics  in  the  secondary  schools  of  this  country.  Each 
year  the  colleges  graduate  how  many  who  are  destined 
to  become  physicists?  Ten  or  twenty?  Then  why  start 
the  rest  of  the  167,000  on  the  road  toward  physics- 
dom?  the  more  so,  since  schooling  is  preparation  for  a 
future  career,  but  education  is  life. 

Those  who  wish  to  make  physics,  consisting  of  both  its 
fundamental  elements,  a  part  of  the  education,  —  namely, 
a  part  of  the  life  of  the  pupil,  —  must  consider  that 
life  in  two  directions.  In  the  first  place,  we  must  con- 
sider the  life  when  he  comes  into  the  physics  class ;  and, 
in  the  second  place,  we  must  consider  his  career  after 
he  leaves  the  physics  class.  We  must  then  seek  to  adapt 
the  work  to  the  condition  of  the  pupil  when  he  enters, 


212  THE  TEACHING  OF  PHYSICS 

and  to  conduct  the  work  during  his  stay  in  such  a  way 
that  he  carries  with  him  when  he  leaves  the  greatest 
possible  quantity  of  knowledge  and  ideals  that  will  be 
of  real  service  to  him  later.  The  working  hypotheses  of 
the  new  education,  as  described  in  the  preceding  chap- 
ters, give  many  suggestions  and  fruitful  hints  as  to  how 
this  may  be  done.  The  most  important  of  these  may 
be  summarized  as  follows :  — 

In  order  to  bring  physics  close  to  the  past  life  of  the 
pupil,  it  is  necessary  that  he  perceive  no  sudden  dis- 
continuity in  his  experiences  with  the  physical  world 
when  he  begins  the  work.  This  means  that  the  phenom- 
ena discussed  and  the  method  of  reasoning  used  at  the 
start  should  be  those  of  the  "  plain  man."  This  close 
connection  with  the  industrial  basis  may  be  gradually 
loosened  as  the  work  proceeds,  but  it  is  very  essential  to 
establish  it  and  make  it  close  at  the  beginning. 

In  order  that  physics  remain  an  important  factor  in 
the  after  life  of  the  pupil,  it  is  necessary  that  the  disci- 
pline and  training  received  in  the  physics  class  be  of  the 
transferable  kind.  This  makes  it  necessary:  (i)  that 
the  pupil  be  inspired  with  the  spirit  of  wonder.  This 
is  accomplished  when  the  solution  of  the  problems  set 
appeals  to  him  as  being  worth  while,  and  he  loses  him- 
self in  the  work  of  solving  them.  (2)  The  pupil  must 
acquire  a  conscious  ideal  of  the  scientific  method  of 


THE   CONCRETE   PROBLEM  213 

solving  problems.  This  is  not  accomplished  by  didactic 
teaching  of  a  logical  setting  forth  of  the  supposed  steps 
of  the  process.  It  may  be  accomplished  by  repeatedly 
showing  the  pupil  that  this  method  always  gives  the 
most  expedient  solution  of  the  problems  that  are  signifi- 
cant to  him  and  whose  solution  he  is  seeking  with  a 
spirit  of  wonder. 

89.  The  Purpose  of  Physics  Teaching.  —  These  sum- 
maries of  the  working  hypotheses  under  which  physics 
may  hope  to  become  part  of  a  genuine  democratic  edu- 
cation define  for  us  the  aim  of  teaching  physics  for  pur- 
poses of  general  education  in  the  following  way :  — 

I.  The  purpose  of  teaching  physics  is  to  assist  the 
pupils  in  acquiring  the  benefits  of  physics  to  the  fullest 
possible  degree. 

The  benefits  of  physics  are  of  two  kinds :  they  consist 
in  the  acquisition  of 

1.  Useful  knowledge  of  physical  phenomena. 

2.  Discipline  in  the  methods  of  acquiring  this  useful 
knowledge. 

Knowledge  of  physical  phenomena  is  useful  in  pro- 
portion as  it  is  definite  and  quantitative.  Definite  and 
quantitative  knowledge  of  physical  phenomena  is  es- 
sential to  every  one  in  controlling  his  environment,  in 
predicting  consequences,  and  in  making  judgments  that 
shall  have  the  greatest  possible  degree  of  validity. 


214  THE  TEACHING  OF  PHYSICS 

Discipline  in  the  methods  of  acquiring  this  useful 
knowledge  results  not  only  in  skill  in  weighing  evidence 
and  in  criticising  and  testing  data,  in  open-mindedness 
or  the  ability  of  holding  conclusions  tentatively  and  of 
altering  them  whenever  new  evidence  demands  it,  and 
in  the  ability  of  predicting  consequences  and  of  making 
judgments  that  shall  have  the  greatest  possible  degree 
of  validity ;  but  also  in  self-forgetfulness,  perseverance, 
self-respect,  and  resourcefulness  in  the  face  of  difficulties. 

II.  Knowledge  of  physical  phenomena  and  discipline 
in  acquiring  it  may  be  either  specific  or  general. 

Specific  knowledge  of  physical  phenomena  is  that 
secured  from  the  study  of  physics  apart  from  its  bearings 
on  other  activities  of  life.  This  specific  knowledge  be- 
comes more  general  in  proportion  as  it  has  elements  in 
common  with  and  is  associated  with  facts  and  experi- 
ences in  other  fields  of  activity.  It  may  be  called  gen- 
eral only  when  it  is  interwoven  with  the  widest  possible 
range  of  knowledge  and  experience. 

In  like  manner,  discipline  in  the  methods  of  acquiring 
this  knowledge  is  specific  when  received  while  acquiring 
specific  knowledge.  It  may  be  acquired  by  repeated 
use  of  the  method  in  solving  specific  problems  in  physics. 
It  becomes  more  general  as  the  specific  knowledge  be- 
comes more  general,  and  as  a  conscious  ideal  of  the 
method  is  formed  and  made  general.  This  conscious 


THE  CONCRETE  PROBLEM          215 

ideal  of  method  is  acquired  and  made  general  in  pro- 
portion as  the  problems  solved  by  it  appear  to  the  in- 
dividual as  being  worth  while,  and  in  proportion  as  he 
strives  for  their  solution  under  the  impulse  of  the  spirit 
of  wonder,  which  fosters  in  him  true  purposes  and  mo- 
tives of  his  own. 

III.  A  student  acquires  the  benefits  of  physics  to  the 
fullest  possible  degree  only  when  both  his  knowledge 
and  his  discipline  in  methods  of  acquiring  it  have  be- 
come general. 

90.  The  Prejudices  of  Our  Schooling.  —  The  concrete 
problem  before  the  physics  teachers  is  that  of  experi- 
mentally testing  this  statement  of  the  purposes  of  physics 
teaching  with  the  idea  of  finding  out  how  far  it  can  be 
put  into  practice  and  in  what  ways  it  can  be  improved. 
This  is  no  easy  task,  since  the  first  essential  of  a  scientific 
test  is  that  the  one  who  makes  it  be  free  from  bias  and 
prejudice ;  and  this  means  freeing  the  mind  from  tradi- 
tions and  habits  of  long  standing.  We  have  had  it  so 
everlastingly  drummed  into  us  that  it  is  our  function 
to  teach  only  the  "  facts  and  principles  of  elementary 
physics"  that  it  is  very  difficult  to  realize  that  this 
may  be  accomplished  best  by  beginning  with  and  making 
copious  use  of  the  facts  and  experiences  of  daily  life. 
Besides,  the  method  here  called  for  enables  the  teacher 
to  "  cover  "  less  ground,  —  fewer  pages  of  the  text,  or  a 


2l6  THE  TEACHING  OF  PHYSICS 

lesser  number  of  the  aforementioned  facts  and  princi- 
ples. 

But  this  freeing  of  the  mind  from  the  prejudices  of 
our  past  schooling,  while  difficult,  is  not  impossible.  In 
several  communities  teachers  have  already  done  it  and 
begun  the  much  needed  experimentation.  It  will  not 
be  long  before  the  excuse  that  syllabi  and  college  entrance 
examinations  compel  adherence  to  traditional  methods 
will  be  wholly  beside  the  mark,  especially  in  the  schools 
supported  by  public  funds.  The  spirit  of  physics  is 
not  composed  of  Newton's  laws  of  motion,  Boyle's  law, 
et  al.;  and  this  spirit  cannot  be  imparted  to  pupils  by 
imposing  on  them  these  ideas,  arranged  in  a  logical  sys- 
tem, to  be  learned  by  fair  means  or  foul.  The  spirit  of 
physics  is  the  intuition  of  universal  relatedness,  which  the 
pupils  already  have ;  and  the  function  of  physics  teaching 
is  to  assist  them  in  making  that  intuition  concrete  and 
in  proving  its  validity.  It  took  physics  three  hundred 
years  to  do  this,  and  we  must  not  expect  the  pupils  to  do 
it  in  twenty  minutes.  We  must  partake  of  the  naive 
skepticism  of  the  Sunday  school  boy  who  bet  that  even 
the  Almighty  could  not  make  a  two-year-old  calf  in  ten 
minutes.  The  remaining  chapters  present  one  way  in 
which  this  spirit  of  physics  may  be  cultivated  and  made 
concrete  among  the  pupils,  without  inhibiting  the  pos- 
sibility of  transferable  discipline.  There  are  many 


THE  CONCRETE  PROBLEM          217 

other  possible  ways  of  doing  this,  and  it  is  hoped  that 
others  will  be  discovered  in  the  near  future. 

SUPPLEMENTARY  READINGS 

BAGLEY,  W.  C.    Educational  Values,  Chapters  I-VI.    New  York, 

Macmillan,  1911. 
HANUS,  P.  H.    Educational  Aims  and  Educational  Values.    Boston, 

Houghton  Mifflin. 

Beginnings  in  Industrial  Education,  Chapters  I-IV.     Bos- 
ton, Houghton  Mifflin,  1908. 

GRIGGS,  EDWARD  H.  The  New  Humanism.  New  York,  Huebsch, 
1900. 

Moral  Education.    New  York,  Huebsch,  1902. 

HALL,  G.  STANLEY.    Adolescence,  Vol.  II,  Chapters  XII,  XVI, 

New  York,  Appleton,  1905. 
—    Educational  Problems,  Vol.  I,  Chapter  VIII.    New  York, 

Appleton,  1911. 
MABIE,   H.   W.     Essays  on  Nature  and  Culture.    New  York, 

Dodd,  Mead,  1896. 
O'SHEA,  M.  V.    Dynamic  Factors  in  Education,  Chapters  I-V, 

also  Bibliography.     New  York,  Macmillan,  1906. 

Social  Development    and    Education.     Boston,    Houghton 

Mifflin,  1909. 

DAVENPORT,  E.    Education  for  Efficiency.    Boston,  Heath,  1909. 
OSTWALD,  W.    Grosse  Manner.    Leipzig,  Akademische  Verlagsge- 
selschaft,  1909. 

Die  For derung  desT ages.    Akad.  Verlagsgesels.,  1911. 

LAVISSE,  E.    L1  Education  de  la  Democratic.     Paris,  Alcan,  1903. 
Conferences  du  Musee  Pedagogique,  par  M.  Liard,  Poincare,  et  al. 

Paris,  Imprimerie  National,  1904. 

A.  GUTZMER.  Die  Tatigkeit  der  Unterrichtskommission  der  Gesel- 
schaft  deutscher  Naturforscher  und  Aerzte.  Leipzig,  Teubner, 
1908. 


CHAPTER  X 
THE  ORGANIZATION  OF  THE  COURSE 

91.  Simplicity  and  Unity.  —  Opinions  differ  as  to 
whether  the  class  work  in  physics  should  be  organized 
about  the  laboratory  work  as  a  center,  or  vice  versa. 
The  question  has  been  much  debated  whether  laboratory 
experiments  should  verify  and  exemplify  facts  and  laws 
first  discussed  in  class,  or  whether  the  facts  and  laws 
should  be  first  met  with  in  the  laboratory  and  discussed 
in  class  afterwards.  The  conclusion  of  this  debate  seems 
to  be  that  it  is  six  to  one  and  half  a  dozen  to  the  other ; 
if  the  facts  and  laws  are  first  discussed  in  class,  the  pupils 
do  the  laboratory  work  more  intelligently;  and  if  the 
laboratory  precedes,  they  understand  the  class  work 
better.  But,  while  there  are  differences  of  opinion  on 
this  matter,  all  are  agreed  that  the  class  work  and  that 
of  the  laboratory  must  be  knit  into  a  well  coordinated, 
simple  and  unified  course. 

For  this  reason  the  first  important  question  to  be 
settled  before  devising  a  suitable  course  in  physics  is, 
How  can  it  be  arranged  to  secure  simplicity  and  unity  ? 
In  answering  this  question,  much  help  can  be  secured 

218 


THE  ORGANIZATION  OF   THE   COURSE  219 

from  a  study  of  the  history  of  physics,  as  outlined  in 
Chapters  V  and  VII.  It  was  there  shown  that  the  great 
unifying  idea  in  physics  has  been  the  idea  of  energy ;  and 
that  unity  was  found  in  this  idea  because  of  the  dis- 
covery of  the  constant  relationships  among  the  units 
of  energy,  the  foot  pound,  the  British  thermal  unit, 
and  the  watt-second  (or  the  erg,  the  gram  calorie,  and 
the  watt-second).  Hence  the  concept  of  energy  may 
well  serve  as  the  unifying  idea  of  the  course. 

That  this  concept  also  gives  the  simplest  interpretation 
of  physical  phenomena  is  also  evident  for  the  following 
reasons :  first,  as  Poincare  shows,1  "  though  other 
systems  of  mechanics  are  possible,  their  equations  would 
be  less  simple  than  those  of  the  accepted  mechanics." 
In  like  manner  its  greater  simplicity  is  the  basis  for  our 
choice  of  Euclidean  in  preference  to  non-Euclidean 
geometry.  In  other  words,  simplicity  is  one  of  the  lead- 
ing criterea  of  the  truth  of  scientific  systems.  Second, 
the  central  hypothesis  of  the  Newtonian  mechanics  is 
that  of  central  forces.  However  brilliant  the  success 
of  this  hypothesis  in  celestial  mechanics,  it  leads  to  vast 
complexity  when  applied  to  physical  mechanics.  In 
fact,  it  may  be  said  to  have  broken  down  completely  in 
its  efforts  to  describe  physical  phenomena,  particularly 
irreversible  processes.  It  also  leads  one  to  seek  to  try 

1  Poincare",  Science  and  Hypothesis,  p.  77  (Science  Press,  1905). 


220  THE  TEACHING  OF  PHYSICS 

to  invent  mechanisms  by  which  natural  phenomena  may 
be  supposed  to  be  produced,  and  this  has  led  away  from 
true  physics,  which  seeks  only  to  determine  the  quanti- 
tative relations  among  the  elements  of  phenomena,  into 
speculations  about  "  centers  of  force,"  the  "  nature  of 
atoms,"  and  the  like. 

It  has  been  urged  that  these  speculations  delight  stu- 
dents and  set  them  to  thinking.  This  is  true,  provided 
you  call  speculation  thinking.  The  Greeks  were  fond 
of  this  sort  of  thinking,  and  the  scientific  value  of  their 
Platonic  thought  has  already  been  sufficiently  explained. 
It  is  much  more  aristocratic  and  lazy  to  speculate  than 
it  is  to  find  out  by  patient  experimenting  just  what 
things  will  actually  do.  Besides,  as  Poincare  shows : 1 
"  When  a  phenomenon  obeys  the  two  principles  of  energy 
and  of  least  action,  it  admits  of  an  infinity  of  mechanical 
explanations.  But  this  is  not  enough :  for  a  mechani- 
cal explanation  to  be  good,  it  must  be  simple ;  for  choos- 
ing it  among  all  which  are  possible,  there  should  be  other 
reasons  besides  the  necessity  of  making  a  choice.  Well, 
we  have  not  as  yet  a  theory  satisfying  this  condi- 
tion and  consequently  good  for  something.  Must  we 
lament  this  ?  That  would  be  to  forget  what  is  the  goal 
sought;  this  is  not  mechanism;  the  true,  the  sole  aim 
is  unity." 

1  Poincar£,  Science  and  Hypothesis,  p.  124. 


THE  ORGANIZATION  OF  THE  COURSE  221 

92.  Mechanism.  —  Most  teachers  will  object  to  aban- 
doning the  attempt  to  teach  high  school  pupils  the  latest 
theories  of  the  mechanism  of  atoms  and  the  kinetic 
theory  of  gases.  It  will  be  urged  that  men  like  Max- 
well and  Kelvin  made  free  use  of  such  mechanisms  and 
were  led  thereby  to  many  fruitful  results.  This  may  be 
perfectly  true  of  expert  physicists  like  those  mentioned, 
although  Duhem  casts  serious  doubts  on  this  idea.1 
But  whether  they  use  mechanisms  usefully  or  not,  ex- 
perts know  how  to  hold  speculation  and  fact  distinct 
in  their  minds,  and  to  use  the  former  to  discover  the 
latter.  The  high  school  pupil  does  not  know  this.  He 
memorizes  the  words  that  express  the  theories  and  the 
speculations  and  the  laws,  and  regards  them  all  to  be  of 
equal  validity  and  importance.  If  you  doubt  this,  ask 
a  physics  class  what  happens  when  you  compress  a 
given  mass  of  gas  to  half  its  volume,  and  see  how  many 
will  attempt  to  tell  what  the  molecules  will  do  during 
the  action,  and  how  many  will  tell  how  the  factors  whose 
relations  have  been  determined  by  measurement  will 
vary.  Mechanism  is  all  very  well  for  expert  physicists ; 
it  is  also  permissible  to  indulge  in  it  now  and  then  with 
beginners,  provided  they  understand  clearly  that  it  is 
all  speculation.  Let  them  play  Greek  once  in  a  while  if 

1  Duhem,  La  Theorie  Physique,  pp.  149^.  (Paris,  Chevalier  et  Rivi&re, 
1906). 


222  THE  TEACHING  OF  PHYSICS 

they  want  to,  but  do  not  let  them  be  beguiled  into  con- 
fusing this  pastime  with  the  serious  business  of  physics. 
In  other  words,  do  not  let  them  confuse  speculation  with 
demonstration  and  objective  knowledge. 

93.  The  Fundamental  Principles.  —  But  if  we  aban- 
don the  idea  of  trying  to  penetrate  into  the  mechanism 
of  phenomena  by  the  use  of  the  theory  of  central  forces, 
what  shall  be  substituted  for  it?  Poincare  suggests  the 
following : 1  "  Nevertheless,  a  day  arrived  when  the 
conception  of  central  forces  no  longer  appeared  sufficient. 
What  was  done  then?  The  attempt  to  penetrate  into 
the  detail  of  the  structure  of  the  universe,  to  isolate  the 
pieces  of  this  vast  mechanism,  to  analyze  one  by  one 
the  forces  which  put  them  in  motion,  was  abandoned, 
and  we  were  content  to  take  as  guides  certain  general 
principles,  the  express  object  of  which  is  to  spare  us  this 
minute  study. 

"  Suppose  that  we  have  before  us  any  machine ;  the  ini- 
tial wheel  work  and  the  final  wheel  work  alone  are  visible, 
but  the  transmission,  the  intermediary  wheels  by  which 
the  movement  is  communicated  from  one  to  the  other, 
are  hidden  in  the  interior  and  escape  our  view.  Do 
we  say  that  it  is  impossible  for  us  to  understand  any- 
thing about  this  machine,  so  long  as  we  are  not  permitted 
to  take  it  to  pieces?  You  know  well  we  do  not,  and 

1  PoincarS,  I.e.,  p.  173. 


THE  ORGANIZATION   OF  THE   COURSE  223 

that  the  principle  of  the  conservation  of  energy  suffices 
to  determine  for  us  the  most  interesting  point.  We 
easily  ascertain  that  the  final  wheel  turns  ten  times  less 
quickly  than  the  initial  wheel ;  since  these  two  wheels 
are  visible,  we  are  able  thence  to  conclude  a  couple  ap- 
plied to  the  one  will  be  balanced  by  a  couple  ten  times 
greater  applied  to  the  other. 

"  Well,  in  regard  to  the  universe,  the  principle  of  the 
conservation  of  energy  is  able  to  render  us  the  same 
service.  This  is  also  a  machine,  much  more  complicated 
than  all  those  of  industry,  and  of  which  almost  all  parts  are 
profoundly  hidden  from  us ;  but  in  observing  the  move- 
ment of  those  that  we  can  see,  we  are  able,  by  the  aid  of 
this  principle,  to  draw  conclusions  which  remain  true 
whatever  may  be  the  details  of  the  invisible  mechanism 
which  animates  them. 

"  The  principle  of  the  conservation  of  energy,  or  the 
principle  of  Mayer,  is  certainly  the  most  important,  but 
it  is  not  the  only  one ;  there  are  others  from  which  we 
are  able  to  draw  the  same  advantage.  These  are :  — 

"The  principle  of  Carnot,  or  the  principle  of  the 
degradation  of  energy. 

"The  principle  of  Newton,  or  the  principle  of  the 
equality  of  action  and  reaction. 

"The  principle  of  relativity,  according  to  which  the 
laws  of  physical  phenomena  should  be  the  same,  whether 


224  THE  TEACHING  OF  PHYSICS 

for  an  observer  fixed,  or  for  an  observer  carried  along 
in  such  a  motion. 

"  The  principle  of  the  conservation  of  mass,  or  princi- 
ple of  Lavoisier. 

"  I  would  add  the  principle  of  least  action. 

"  The  application  of  these  five  or  six  general  principles 
to  the  different  physical  phenomena  is  sufficient  for  our 
learning  of  them  what  we  could  reasonably  hope  to 
know  of  them." 

These,  then,  are  the  principles  in  modern  physics 
which  supersede  the  hypothesis  of  central  forces  in  New- 
tonian physics.  It  is  perfectly  true  that  in  acquiring 
these  principles  physics  traveled  via  the  doctrine  of 
central  forces.  But  is  that  the  shortest  and  quickest 
road  ?  Now  that  these  principles  have  been  established, 
cannot  the  beginner  be  led  to  acquire  some  realization 
of  their  meaning  in  a  more  direct  way?  Perhaps  if  the 
hypothesis  of  central  forces  had  not  yielded  such  mar- 
velous results  when  applied  by  Newton  to  celestial  me- 
chanics, these  principles  might  have  been  established  by 
physics  in  a  more  direct  manner  by  following  the  lead 
of  Stevin,  Galileo,  and  Huyghens.  The  brilliancy  of 
Newton's  achievements  in  treating  a  frictionless  system 
may  have  given  men  an  exaggerated  idea  of  their  value 
in  treating  systems  with  constraints. 

94.   Objectivity  Necessary.  —  Be  that  as  it  may,  the 


THE  ORGANIZATION  OF  THE  COURSE  225 

function  of  the  physics  teacher  of  to-day  is  to  assist  the 
pupils  in  acquiring  the  benefits  of  physics  to  the  fullest 
possible  degree  in  the  short  time  at  his  disposal.  He  will 
surely  do  this  most  effectively  if  he  will  aim  directly  at 
the  big  and  dynamic  things  in  modern  physics.  In  doing 
this,  the  closer  he  sticks  to  what  is  fundamentally  real 
and  objective,  the  more  likely  he  will  be  to  succeed; 
and  "  The  sole  objective  reality  consists  in  the  relations 
of  things  whence  results  the  universal  harmony.  These 
are  objective  because  they  are,  will  become,  or  will 
remain,  common  to  all  thinking  beings."  1  "  Besides, 
if  we  study  mechanics,  it  is  to  apply  it ;  and  we  can 
apply  it  only  if  it  remains  objective.  ...  It  is  therefore, 
above  all,  with  the  objective  side  of  the  principles  that 
we  must  be  familiarized  early,  and  that  can  be  done  only 
by  going  from  the  particular  to  the  general,  instead  of  the 
inverse."  2  Finally :  "  When  we  say  force  is  the  cause 
of  motion,  we  talk  metaphysics ;  and  this  definition,  if 
one  were  content  with  it,  would  be  absolutely  sterile. 
For  a  definition  to  be  of  any  use,  it  must  teach  us  to 
measure  force ;  moreover  that  suffices  ;  it  is  not  at  all 
necessary  that  it  teach  us  what  force  is  in  itself,  nor 
whether  it  is  the  cause  or  the  effect  of  motion."  3 
To  summarize :  i .  The  really  objective  things  in 

1  Poincare,  The  Value  of  Science,  p.  140. 

2  Poincar£,  Science  and  Hypothesis,  p.  100.  8  Ibid.,  p.  73. 

Q 


226  THE  TEACHING  OF  PHYSICS 

physics  are  the  quantitative  relations  among  phenomena, 
as  determined  by  measurement.  2.  The  pupil  shows 
the  true  spirit  of  physics  when  he  becomes  absorbed 
in  its  objective  side,  i.e.  in  determining  numerical 
relations  among  phenomena.  3.  Throughout  the  course 
the  pupil  must  remain  close  to  the  objective  side,  i.e.  to 
the  relations  that  can  be  measured,  and  must  proceed 
from  special  cases  to  more  general  relations.  4.  Defini- 
tions, to  be  of  any  value,  must  teach  us  how  to  measure 
the  thing  defined. 

/j  95.  Definitions.  —  These  ideas,  together  with  those 
developed  in  Chapters  V  to  IX,  point  out  the  way  to 
organizing  a  really  vital  course  in  physics.  There  are 
many  ways  of  doing  this,  but  the  following  plan  of 
treating  the  energy  principle  may  serve  as  an  example 
of  the  general  method  of  going  at  it. 

Since  the  essence  of  the  work  is  to  consist  in  the 
measurement  of  related  factors,  it  is  necessary  at  the 
start  to  define  the  factors  whose  relations  are  to  be 
determined.  This  means  that  we  must  tell  how  they 
are  measured.  This  should  not,  however,  be  done  in 
the  usual  way;  namely,  by  an  abstract  discussion  of 
the  metric  system  and  the  mere  statement  of  the 
definitions  of  the  absolute  units.  As  Poincare  points 
out : 1  "  How  can  we  find  a  concise  statement  which 

1  PoincarS,  Science  el  Melhode,  p.  139. 


THE  ORGANIZATION  OF  THE   COURSE  227 

will  satisfy  at  once  the  inviolable  rules  of  logic,  our  desire 
to  understand  the  place  of  the  new  idea  in  the  ensemble 
of  science,  and  our  need  of  thinking  in  images?  Most 
frequently  this  cannot  be  done,  and  that  is  why  it  is 
not  enough  to  state  a  definition ;  it  is  necessary  to  pre- 
pare the  way  for  it  and  to  justify  it.  ...  A  definition 
is  presented  to  us  as  a  convention ;  but  most  people  re- 
volt if  you  try  to  impose  it  on  them  as  an  arbitrary  con- 
vention. .  .  .  Usually  mathematical  definitions  are  veri- 
table edifices  constructed  of  many  simpler  ideas.  But  why 
are  these  elements  arranged  in  this  way,  when  a  thousand 
other  arrangements  are  possible?  Is  it  by  caprice?  If 
not,  why  has  this  particular  arrangement  more  right  to 
live  than  all  the  rest?  To  what  need  does  it  respond? 
How  was  it  foreseen  that  it  would  play  an  important 
role  in  the  development  of  science?  Is  there  in  nature 
any  familiar  object  which  is,  as  it  were,  an  indefinite  and 
gross  image  of  it?  " 

Poincare  then  shows  that  if  you  wish  to  make  satis- 
factory answer  to  such  questions,  you  will  have  to  explain 
the  analogies  that  have  led  to  the  definitions,  and  then 
concludes :  "If  the  definition  is  sufficiently  rigorous 
to  please  the  logician,  its  justification  will  content  the 
intuitive.  But  it  is  better  to  do  still  more.  Whenever 
it  is  possible,  the  justification  will  precede  the  statement 
of  it,  and  will  prepare  the  way  for  it ;  the  student  will  be 


228  THE  TEACHING  OF  PHYSICS 

led  to  the  general  statement  by  a  study  of  several  partic- 
ular examples." 

96.  How  Define  Work  ?  —  If  we  follow  this  excellent 
advice,  we  will  begin  the  discussion  by  preparing  the  way 
for  a  definition  of  work  —  a  definition  consisting  of  a 
statement  of  how  work  is  measured.  Since  we  must  at 
the  start  keep  close  to  general  experiences  and  seek  to 
produce  a  fork-road  situation  in  which  thinking  begins,  we 
might  well  begin  in  some  such  way  as  this :  Is  it  more 
work  to  climb  straight  up  a  tree  than  to  climb  up  to 
the  same  height  on  a  ladder?  Why?  Is  it  more  work 
to  climb  to  the  third  floor  up  a  vertical  fire  escape  or  to 
walk  up  the  stairs  to  the  same  height?  Why?  Does 
it  require  more  work  to  slide  a  cake  of  ice  up  an  inclined 
plane  into  an  ice  house  than  it  does  to  lift  it  vertically  to 
the  same  height  ?  Why  ?  What  do  you  mean  by  work  ? 
Are  scrubbing  floors,  painting  houses,  sawing  wood, 
planing  boards,  pumping  water,  plastering  walls,  filing 
metals,  all  forms  of  work?  What  are  their  common 
elements  that  make  us  classify  them  as  work  ? 

Having  made  it  evident  that  work  consists  in  push- 
ing, pulling,  or  lifting  something  for  some  distance 
against  resistance,  we  show  that  in  order  to  answer  the 
questions  first  raised,  we  must  needs  measure  work.  If 
by  some  such  procedure  as  the  foregoing  a  need  for 
measuring  work  has  been  created,  the  pupils  will  have 


THE  ORGANIZATION  OF  THE  COURSE  229 

no  difficulty  in  following  an  argument  of  this  kind :  Work 
is  done  when  one  brick  is  lifted  one  foot.  How  much 
more  work  is  done  when  two  bricks  are  lifted  one  foot? 
When  three  bricks  are  lifted  one  foot  ?  How  much  more 
work  is  done  when  one  brick  is  lifted  two  feet?  When 
two  bricks  are  lifted  two  feet?  The  amount  of  work 
done  thus  depends  on  the  number  of  bricks  lifted  and 
the  distance  through  which  they  are  lifted.  If  the 
bricks  weighed  nothing,  it  would  be  no  work  to  lift  them. 
It  is,  then,  the  weight  and  the  distance  that  determines 
the  amount  of  work.  But  weight  is  measured  in  pounds 
and  distance  is  measured  in  feet,  so  work  is  measured  by 
the  product  of  pounds  weight  times  feet. 

This  idea  may  then  be  extended  to  horizontal  work 
by  showing  that  horizontal  forces  may  be  replaced  by 
weights  on  the  ends  of  strings  that  pass  over  pulleys, 
or  by  pulls  measured  by  spring  balances.  Thus  a 
definition  of  force  as  anything  that  may  be  measured  by  a 
spring  balance  in  pounds  weight  (or  grams  weight)  is 
finally  reached. 

It  then  remains  to  show  that  the  force  and  the  distance 
must  be  measured  in  the  same  direction.  This  may  well 
be  taken  for  granted  at  the  start,  and  explained  after 
some  of  the  experiments  have  been  done. 

97.  Problems  that  Require  Measurements.  —  Having 
now  defined  work,  by  showing  how  it  is  measured,  we 


230  THE  TEACHING  OF  PHYSICS 

are  ready  to  take  up  the  problems  proposed.  It  will 
be  noted  that  these  are  of  the  sort  that  cannot  be  answered 
without  measurement.  In  order  to  answer  them  definitely, 
recourse  must  be  had  to  experiment.  Since  a  block  of 
ice  and  an  ice  house  are  not  available,  we  let  a  block  of 
wood  represent  the  ice,  and  a  sloping  board  the  inclined 
plane,  and  pull  the  block  up  the  plane  uniformly  with  a 
spring  balance.  The  number  of  pounds  force  indicated 
by  the  balance  multiplied  by  the  number  of  feet  through 
which  the  block  is  pulled  along  the  plane  measures  the 
work  done.  The  weight  of  the  block  multiplied  by  the 
height  of  the  plane  measures  the  work  done  in  lift- 
ing it  vertically.  Many  pupils  are  surprised  to  see  how 
much  greater  the  former  is  than  the  latter. 

Why  does  it  take  so  much  more  work  to  pull  the  block 
up  the  plane?  Can  this  difference  in  the  amounts  of 
work  be  lessened  in  any  way?  Try  placing  the  block 
on  wheels.  This  expedient  brings  the  two  amounts  of 
work  nearer  together.  Cover  the  plane  with  a  strip  of 
glass;  further  improvement  results.  We  thus  see  that 
as  we  perfect  the  machine  the  two  amounts  of  work 
grow  more  nearly  equal.  We  may  conclude  that  if  we 
could  make  an  ideally  perfect  machine,  the  two  would 
be  equal. 

98.  Efficiency.  —  We  are  now  ready  for  more  defi- 
nitions. The  useful  work  done  by  the  machine  is 


THE  ORGANIZATION  OF  THE   COURSE  231 

called  the  output  or  work  out;  in  this  case,  it  is  the 
product  of  the  weight  and  the  vertical  height  of  the 
plane.  The  actual  work  done  is  called  the  input  or  work 
in.  The  efficiency  of  the  machine  is  the  fraction  ob- 
tained by  dividing  the  output  by  the  input.  Since  in 
practical  cases  the  input  is  greater  than  the  output,  the 
efficiency  of  the  inclined  plane  is  less  than  unity. 

We  may  now  ask  whether  a  wheel  and  axle,  a  set  of 
pulleys,  or  a  combination  of  levers  might  be  used  with 
greater  success  in  lifting  ice  into  the  ice  house.  This 
again  is  a  problem  that  cannot  be  answered  without 
making  measurements.  We  have  to  measure  the 
efficiencies  of  the  particular  wheel  and  axle  or  the  par- 
ticular pulleys  that  it  is  proposed  to  substitute  for  the 
inclined  plane.  This  investigation  may  lead  to  a  com- 
parison of  various  sets  of  pulleys,  a  study  of  how  they 
may  be  improved,  leading  to  the  same  conclusion  as 
before;  namely,  in  the  ideal  case,  the  input  and  the 
output  would  be  equal,  but  in  every  real  case  the  input 
is  greater  than  the  output  and  the  efficiency  is  less 
than  unity. 

99.  Summary.  The  Work  Principle.  —  This  method 
of  treatment  fulfills  the  pedagogical  and  scientific  re- 
quirements that  were  discussed  in  the  previous  chapters. 
It  begins  with  the  daily  experiences :  it  produces  a 
situation  in  which  a  problem  is  defined ;  the  problem  will 


232  THE  TEACHING  OF  PHYSICS 

generally  be  significant  if  the  teacher  has  not  tried  to 
tell  the  answer  in  advance ;  the  answer  is  unknown  to 
the  teacher  and  cannot  be  obtained  without  measure- 
ments; the  definitions  of  the  units  of  measurement 
are  justified  in  advance ;  the  ideal  case  or  law  is  found 
by  a  series  of  approximations;  the  laboratory  assumes  its 
correct  function  as  the  place  in  which  to  seek  information 
that  cannot  be  secured  elsewhere,  and  the  whole  dis- 
cussion leads  somewhere  in  physics,  —  namely,  to  the 
work  principle,  which  is  repeated  and  encountered  in 
several  different  ways. 

An  admirable  conclusion  of  this  discussion  consists  in 
showing  Galileo's  pendulum  experiment,  and  drawing  as 
many  conclusions  from  it  as  the  pupils  are  able  to  draw. 
Such  are :  in  measuring  work,  force  and  distance  must  be 
measured  in  the  same  direction;  the  center  of  gravity 
seeks  the  lowest  level;  the  idea  of  inertia;  work  done 
by  or  against  gravity  depends  on  vertical  difference  of 
level  and  not  on  the  path  from  one  level  to  the  other. 

After  the  idea  of  the  work  principle  is  well  grasped  in  its 
relations  to  simple  machines,  we  may  pass  on  to  work  done 
by  fluids.  If  a  water-power  plant  exists  in  the  neighbor- 
hood, a  visit  to  it  would  probably  be  the  most  effective 
starting  point.  If  not,  secure  several  small  water  motors, 
and  ask  the  class  which  is  the  best  one.  This  leads 
again  to  a  necessity  for  measurements,  and  for  methods  of 


THE  ORGANIZATION  OF  THE  COURSE  233 

measuring  work  done  by  fluids  and  that  done  by  motors. 
It  may  lead  to  a  study  of  the  conditions  of  maximum 
efficiency  of  one  motor,  and  those  of  perfecting  the  ma- 
chine so  as  to  increase  its  efficiency.  This  idea  of 
maximum  efficiency  is  valuable  as  giving  a  first  inkling 
of  the  meaning  of  the  principle  of  least  action.  The 
final  result  of  it  all  is,  the  output  is  greater  than  the 
input,  or  the  efficiency  is  less  than  unity. 

100.  Problems  in  Heat.  —  Since  the  example  we  are 
trying  to  describe  is  that  of  the  presentation  of  the 
energy  principle,  we  pass  over  the  treatment  of  the 
other  principles  of  fluids  and  continue  with  those  ideas 
in  the  subject  of  heat  which  bear  on  this  immediate 
question.  In  heat  it  may  be  well  to  begin  with  some  such 
question  as  this :  Which  is  the  most  efficient  kettle,  one 
of  iron,  one  of  aluminum,  one  of  enameled  ware,  one 
of  copper,  or  one  of  tin?  Or  which  is  the  most  efficient 
kind  of  a  gas  burner,  a  Bunsen  burner  or  one  on  the 
kitchen  stove?  These  questions  define  problems  that 
are  significant  to  most  pupils  because  close  to  the  daily 
life.  They  also  make  measurement  necessary,  and  pre- 
pare the  way  for  the  definition  of  the  units  of  quantity  of 
heat  (the  British  thermal  unit  or  the  gram  calorie). 
The  answers,  however,  come  out,  not  as  true  efficiencies, 
but  in  terms  of  British  thermal  units  per  minute  or  in 
gram  calories  per  cubic  foot  of  gas.  To  reduce  them  to 


234  THE  TEACHING  OF  PHYSICS 

true  efficiencies,  we  must  find  the  number  of  gram 
calories  per  cubic  foot  of  gas.  This  leads  to  the  idea  of 
thermal  efficiency  as  the  ratio  of  useful  heat  retained  to 
total  heat  used.  This  ratio  is  again  found  to  be  a  fraction 
whose  value  is  less  than  unity.  This  fact  may  lead  to 
a  study  of  the  conditions  under  which  the  efficiency  may 
be  increased,  if  desired. 

The  steam  engine  furnishes  probably  the  best  approach 
to  the  treatment  of  the  relations  between  heat  and  work. 
Its  history  is  particularly  instructive,  and  its  present 
importance  to  the  world's  work  is  always  a  fruitful 
topic  for  discussion.  The  steam  engine  depends  upon 
coal,  so  the  value  of  coal  supply  and  the  present  active 
campaign  for  conservation  of  natural  resources  are 
useful  means  of  connecting  the  problem  with  the  daily 
life.  The  real  problem  here  is:  Are  we  wasting  coal? 
Is  the  steam  engine  as  efficient  as  it  might  be  ? 

The  workings  of  the  old  engines,  like  Newcomen's, 
should  first  be  described,  and  the  faults  in  their  con- 
struction noted.  Then  explain  Watt's  devices  for  saving 
heat  and  increasing  the  efficiency,  noting  particularly 
his  recognition  of  the  need  of  a  hot  body  and  a  cold  body 
if  work  is  to  be  secured  by  heat.  Watt's  best  engine, 
however,  consumed  ten  pounds  of  coal  per  horse-power 
hour.  Since  Watt's  time,  engines  have  been  improved 
until  now  the  locomotive  consumes  about  three  pounds 


THE  ORGANIZATION  OF  THE   COURSE  235 

of  coal  per  horse-power  hour;  while  a  good  marine 
engine  consumes  about  one  pound  for  the  same  amount  of 
work. 

Is  this  the  limit  of  the  possibilities  in  the  case?  To 
answer  this  we  must  know  what  the  true  efficiency  of 
the  engine  is.  Pounds  of  coal  per  horse-power  hour  is 
not  true  efficiency  because  the  input  and  the  output  are 
measured  in  different  units.  By  burning  coal  in  a  calo- 
rimeter, we  can  find  out  how  many  British  thermal  units 
of  heat  are  liberated  by  burning  a  pound  of  coal.  This 
enables  us  to  state  our  efficiency  as  a  ratio  between 
horse-power  hours  and  British  thermal  units ;  but  still 
the  units  are  not  the  same.  Is  it  possible  that  these  two 
quantities  may  be  reduced  to  the  same  units?  Is  there 
any  constant  relation  between  the  British  thermal  unit 
and  the  foot  pound. 

1 01.  Definition  of  Energy.  — We  have  now  prepared 
the  way  for  Joule's  experiment  on  the  mechanical  equiva- 
lent of  heat,  and  for  the  statement  of  the  result.  It  is 
important  here  to  make  clear  the  real  meaning  of  this 
result.  The  experiment  consists  in  doing  a  certain 
number  of  foot  pounds  of  work  on  a  machine  and  getting 
a  certain  number  of  British  thermal  units  in  return. 
The  result  is  important  because  it  shows  that  when  we 
divide  the  number  of  foot  pounds  of  input  by  the  number 
of  British  thermal  units  output,  we  always  get  practically 


236  THE  TEACHING  OF  PHYSICS 

the  same  number,  namely,  778.  The  meaning  of  this 
fact  can  be  grasped  by  considering  the  following  analo- 
gous case. 

If  we  measure  the  edge  of  the  table  in  inches  and  in 
centimeters,  and  divide  the  number  of  centimeters  by 
the  number  of  inches,  we  get  the  result  2.54  centimeters 
per  inch.  Whenever  we  measure  the  same  length  in 
terms  of  these  different  units,  and  divide  the  number 
of  centimeters  by  the  number  of  inches,  we  get  the  same 
constant  ratio,  namely,  2.54.  The  constancy  of  this 
ratio  between  the  units  indicates  that  we  have  been 
measuring  the  same  thing  in  terms  of  the  different  units. 
In  like  manner,  the  constancy  of  the  ratio  between  the 
foot  pound  and  the  British  thermal  unit  indicates  that 
in  these  experiments  of  Joule's  he  was  measuring  the 
same  thing  in  terms  of  different  units.  This  same  thing 
is  what  we  call  energy. 

Having  thus  prepared  the  way  for  the  definition  of 
energy,  we  may  state  it  in  such  a  way  as  this:  en- 
ergy is  measured  in  foot  pounds  or  in  British  thermal 
units.  This  is  the  only  definition  that  has  any  real 
value  in  physics.  To  say  that  "  energy  is  ability  to  do 
work,"  is  to  talk  metaphysics.  It  is  a  perfectly  useless 
statement  both  for  the  pupil  and  for  science.  Its  only 
benefit  is  the  negative  one  of  supplying  the  pupil  with 
a  catch  phrase  which  he  can  repeat  glibly  when  properly 


THE  ORGANIZATION  OF  THE  COURSE  237 

stimulated  to  do  so,  and  which  he  can  use  in  examination 
to  cover  up  effectively  his  real  ignorance.  If  you  begin 
the  course  by  telling  the  class  that  there  are  two  "  en- 
tities "  in  the  world,  matter  and  energy,  and  that  the 
quantity  of  both  is  eternally  fixed,  you  are  trying  to 
make  a  two-year-old  calf  in  two  minutes.  Having 
learned  to  repeat  that  statement,  the  pupil  is  apt  to  think 
he  "  knows  "  everything,  and  further  study  of  physics 
seems  unnecessary.  You  have  given  him  an  "  absolute  " 
and  "  immutable  "  Platonic  thought,  and  blunted  his 
sensitiveness  to  a  real  appreciation  of  the  relatedness 
of  phenomena. 

102.  The  Energy  Principle.  —  But  the  energy  principle 
is  not  yet  complete.  Electricity  remains  to  be  conquered. 
Here  again  it  is  well  to  begin  with  some  such  question  as 
this :  Here  are  several  small  motors ;  which  is  the  most 
efficient?  Your  result  will  be  obtained  in  foot  pounds 
per  watt-second.  This  is  no  real  efficiency,  since  the  units 
are  not  the  same.  Is  it  possible  to  reduce  them  to  the 
same  unit?  Joule's  experiments  with  the  calorimeter 
give  a  constant  relation  between  the  British  thermal  unit 
and  the  watt-second,  namely,  i  British  thermal  unit 
=  1055  watt-seconds.  The  constancy  of  this  ratio  again 
means  that  we  have  been  measuring  the  same  thing  in 
terms  of  different  units;  and  we  expand  our  definition 
of  energy  to  read :  energy  is  the  thing  that  is  measured  in 


238  THE  TEACHING  OF  PHYSICS 

foot  pounds,  in  British  thermal  units,  or  in  watt-seconds. 
The  energy  principle  may  then  be  stated  in  some  such 
way  as  this :  energy  input  =  energy  output.  Or,  if  you 
prefer,  foot  pounds  +  British  thermal  units  +  watt-sec- 
onds input  =  foot  pounds  +  British  thermal  units  +  watt- 
seconds  output. 

103.  Some  Objections.  —  This  method  of  treatment 
will  shock  most  physics  teachers  because  it  is  illogical. 
How  can  pupils  measure  watt-seconds,  they  say,  unless 
they  have  had  the  watt  carefully  denned  by  logical 
steps  beginning  with  the  unit  charge  of  static  electricity, 
which  is  the  simplest  element,  and  proceeding  thence  to 
build  up  the  idea  volt  with  the  help  of  this  unit  charge 
and  the  idea  of  work  previously  defined  in  an  equally 
logical  manner.  The  reply  is  simple.  Give  them  an 
ammeter  and  a  voltmeter  and  a  real  motor  to  test  and 
see  if  they  can  do  it.  And  do  not  forget  that  a  definition 
must  be  justified  in  advance  of  its  statement,  and  that 
a  logical  setting  forth  of  a  process  is  possible  only  after 
the  result  has  been  attained  by  less  formal  and  more 
intuitive  processes.  The  essential  thing  is  to  produce  a 
situation  in  which  thinking  begins ;  when  this  has  been 
accomplished,  the  direction  of  the  thinking  into  useful 
channels  is  not  so  difficult. 

Objection  is  also  made  to  the  method  of  presentation 
here  suggested  as  the  best,  on  the  ground  that  it  is 


THE  ORGANIZATION  OF  THE   COURSE  239 

basely  commercial  and  leads  nowhere  in  physics.  This 
objection  is  perfectly  valid  when  the  work  is  so  done 
as  to  make  the  statement  true.  But  when  practical 
applications  and  the  measurement  of  the  efficiencies  of 
real  machines  is  merely  the  significant  starting  point 
for  the  acquisition  of  a  tolerably  definite  and  concrete 
meaning  of  the  doctrine  of  energy,  who  will  say  that 
the  means  do  not  justify  the  end?  The  more  so,  if 
transferable  discipline  and  an  ideal  of  scientific  method 
has  also  been  secured  in  the  process.  And  although 
this  method  of  treatment  is  here  urged  as  the  only  one 
that  will  enable  physics  to  hold  its  honorable  place  in 
a  system  of  democratic  education,  it  is  more  than  prob- 
able that  it  may  be  a  far  better  system  of  training 
prospective  physicists  than  the  system  now  in  use. 
Experiment  alone  can  settle  this  question,  and  until 
such  experiments  have  been  made,  it  is  useless  to  condemn 
this  method  because  of  the  repugnance  which  all  feel 
toward  changing  well-established  habits  of  thought  and 
action. 

104.  Optics.  —  As  a  second  example  of  the  method 
of  treatment  demanded  by  the  working  hypotheses 
here  set  forth,  consider  the  subject  of  optics.  Here  the 
unifying  idea  cannot  be  that  of  energy,  since  the  treat- 
ment of  optics  from  this  point  of  view  has  not  yet  been 
fully  worked  out.  Unity  may  be  secured  here  in  numerous 


240  THE  TEACHING  OF  PHYSICS 

ways.  We  may  ask :  what  does  light  do  for  me,  and  how 
does  it  do  it  ?  The  personal  uses  of  light  and  of  optical 
instruments  in  seeing  things  and  in  increasing  our  powers 
of  vision  become  the  center  of  the  course.  It  is  of  course 
perfectly  useless  to  begin  this  study  with  a  statement  of 
the  theories  of  ether  and  electromagnetic  vibration, 
or  with  discussions  of  the  "  nature  of  light."  Such 
problems  belong  to  metaphysics;  physics  is  concerned 
with  such  relations  among  the  elements  of  phenomena  as 
can  be  determined  by  observation  and  experiment. 

One  of  the  most  useful  things  that  light  does  for  us  is 
to  enable  us  to  distinguish  objects  from  one  another  and 
to  judge  of  their  relative  positions,  sizes,  and  motions. 
How  does  it  do  this?  How  do  we  detect  differences  in 
direction  and  in  size?  The  sun  and  the  moon  appear 
to  be  of  the  same  size;  a  fly  on  the  window  ten  feet 
away  appears  just  as  big  as  a  man  half  a  mile  away. 
To  one  looking  along  a  straight  railroad  track,  the  rails 
appear  to  be  closer  together  at  a  distance  than  near  by, 
although  they  are  the  same  distance  apart  everywhere. 
There  is  thus  a  difference  between  real  size  and  apparent 
size ;  in  what  does  this  consist  ? 

If  the  work  in  energy  as  previously  described  has 
preceded  the  work  in  light,  the  pupils  should  be  able  to 
grasp  the  problem  as  thus  defined.  If  not,  the  problem 
may  be  defined  more  concretely  by  a  study  of  cameras. 


THE  ORGANIZATION  OF  THE   COURSE  241 

Do  all  cameras  placed  at  the  same  distance  from  an 
object  take  pictures  of  the  same  size  ?  Can  you  take  a 
picture  without  a  lens  ?  Are  all  such  pictures  of  the  same 
size  ?  If  not,  why  not  ?  What  conditions  determine  the 
size  of  the  picture?  The  classroom  experiment  with 
the  pinhole  camera  on  a  large  scale  is  an  effective  source 
of  motivation  here. 

From  working  with  pinhole  and  other  cameras,  the 
pupils  may  soon  be  led  to  see  that  the  visual  angle  is 
determinative  of  the  apparent  size  of  an  object,  and  that 
the  image  always  subtends  the  same  angle  at  the  center 
of  the  opening  or  the  lens;  hence  the  light  travels  in 
straight  lines.  The  visual  angle  of  a  given  object  at  a 
given  distance  is  fixed ;  the  angle  subtended  by  the 
image  is  always  equal  to  the  visual  angle  of  the  object, 
and  so  the  actual  size  of  an  image  for  fixed  object  and 
object-distance  depends  only  on  the  distance  of  the 
image  from  the  pinhole  or  lens.  This  constancy  of  the 
visual  or  lens  angles  of  the  object  is  of  fundamental 
importance  and  may  be  made  the  key  to  the  problems  of 
vision,  thus  giving  unity  to  the  treatment  of  this  topic. 

The  other  factor  in  a  discussion  of  vision  is  that  of 
focal  length.  The  image  in  a  pinhole  camera  is  blurred 
or  fuzzy,  because  each  point  of  the  object  sends  a  cone 
of  light  through  the  pinhole,  and  this  cone  makes  in 
the  image  a  spot  instead  of  a  point.  The  image  is  thus 


242  THE  TEACHING  OF  PHYSICS 

composed  of  an  array  of  overlapping  spots  instead  of 
points;  and  it  is,  therefore,  blurred.  A  lens  that  is 
thicker  in  the  middle  than  it  is  at  the  rim  reduces 
these  spots  in  the  image  nearly  to  points,  and  so  the 
image  becomes  clearer,  provided  the  screen  that  receives 
the  image  is  placed  at  one  particular  position  called  the 
focus.  The  size  of  the  image  in  this  position  is  the  same 
whether  the  lens  is  used  or  not ;  the  lens  merely  makes 
the  image  clearer.  When  the  difference  in  thickness 
between  the  middle  and  the  rim  of  the  lens  is  large,  the 
focus  is  nearer  the  lens ;  and  when  this  difference  is 
small,  the  focus  is  farther  off.  Hence  long  focus  lenses 
produce  larger  images  of  the  same  object  at  a  given  dis- 
tance than  do  short  focus  lenses,  although  the  visual  or 
lens  angles  are  the  same  for  each. 

105.  Theories  Unnecessary.  —  It  will  be  noted  that 
this  discussion  requires  neither  the  wave  theory  nor  the 
ray  theory  of  light.  It  enables  the  pupil  to  acquire  many 
useful,  consistent,  and  definite  ideas  as  to  vision  and 
cameras.  On  this  foundation  it  is  easy  to  proceed  to  a 
simple  and  rational  explanation  of  how  the  simple  mi- 
croscope and  the  telescope  enable  us  to  increase  the 
apparent  sizes  of  objects,  of  the  faults  of  eyes,  and  even 
of  the  ideas  of  resolution.  If  the  class  is  interested  in 
this  work,  the  problem  of  finding  how  accurately  the 
lens  reduces  the  spot  of  the  pinhole  camera  to  a  point 


THE  ORGANIZATION  OF  THE  COURSE  243 

leads  readily  to  easy  discussions  of  chromatic  aberration, 
spherical  aberration,  and  astigmatism.  In  other  words, 
although  the  discussion  starts  with  the  immediate  phe- 
nomena of  daily  life,  or  with  the  commercial  camera,  the 
upper  limit  in  physics  at  which  the  work  must  stop  is 
placed  only  by  the  limitations  of  the  teacher,  the  pupils, 
and  the  time. 

Objection  will  be  made  to  the  foregoing  outline  on 
the  ground  that  it  dispenses  with  the  mechanism  of 
image  formation,  and  tries  only  to  develop  clear  ideas 
about  those  relations  between  objects,  images,  and  focal 
lengths  which  are  amenable  to  observation  and  measure- 
ment. Those  who  feel  this  way  about  it  are  urged  to 
produce  diagrams  and  explanations  of  image  formation 
such  that  a  beginner  can  understand  them.  It  is  well 
enough  to  introduce  the  wave  theory  at  the  end,  after 
the  pupils  have  gathered  enough  facts  and  experience 
to  appreciate  it,  but  to  hang  the  whole  discussion  from 
the  start  on  the  wave  theory  is  a  genuine  case  of  putting 
the  cart  before  the  horse.1 

1 06.  Light  and  Electricity.  —  Some  of  the  work  in 
light  may  well  be  closely  annexed  to  that  in  heat  and 
electricity  by  studying  the  efficiencies  of  various  sources 
of  illumination,  such  as  candles,  kerosene,  gas,  and  vari- 

1  For  a  complete  working  out  of  the  ideas  here  presented  for  a  full  year's 
work,  the  reader  is  referred  to  the  Mann  &  Twiss  Physics,  2d  ed.,  Part  I 
(Chicago,  Scott,  Foresman  &  Co.,  1910). 


244  THE  TEACHING  OF  PHYSICS 

ous  kinds  of  electric  lamps.  This  extension  necessitates 
merely  the  addition  of  the  idea  of  photometry.  While 
it  leads  to  no  real  efficiency,  it  gives  interesting  results 
as  to  the  cost  of  the  various  kinds  of  illuminants  per 
candle-power  hour.  There  is  a  great  deal  of  very  valu- 
able laboratory  work  that  may  profitably  be  associated 
with  work  on  this  subject. 

The  topic  of  color  is  always  of  interest  if  approached 
concretely  by  showing  a  group  of  variously  colored  ob- 
jects in  differently  colored  lights.  The  tri-color  printing 
processes  are  always  a  prime  source  of  objective  atten- 
tion. 

107.  Remember  the  Aim,  Unity.  —  Enough  has  been 
said  to  make  clear  the  method  of  treatment  called  for 
by  the  working  hypotheses  of  the  new  education.  It 
must  not  be  inferred  that  the  above  outline  of  this 
method  as  applied  to  the  energy  principle  and  to  optics 
is  an  outline  of  an  entire  year's  course.  Far  from  it. 
Other  principles  and  phenomena  need  treatment  also; 
though  it  is,  of  course,  dear  that  all  of  the  principles 
which  Poincare  mentions  (see  p.  223  ante)  cannot  re- 
ceive treatment  in  a  high  school  course.  If  the  teacher 
remembers  that  physics  does  not  consist  of  a  large  num- 
ber of  detached  fragments  of  facts  and  laws,  and  that 
elementary  physics  is  not  a  totally  different  species  from 
physics,  but  is  the  child  which  grows  later  into  the  man 


THE  ORGANIZATION  OF  THE  COURSE  245 

physics,  he  should  be  able  to  organize  a  course  having 
unity,  significance,  simplicity,  and  real  value  in  the 
lives  of  those  who  must  enter  the  ranks  of  the  world's 
workers. 

SUPPLEMENTARY  READINGS 

MANN,  C.   R.,   and  Twiss,   G.   R.   Physics,   2d  ed.     Chicago, 

Scott,  Foresman,  1910. 
An  elementary  text  in  which  the  principles  here  set  forth  are 

applied. 

WOODHULL,  J.  F.  The  Teaching  of  Physical  Science.  Teachers 
College  Record,  January,  1910.  Pages  27-82  contain  a  num- 
ber of  excellent  examples  of  method  of  presentation. 

Electricity  and  its  Everyday  Uses.    New  York,  Doubleday, 

Page,  1911. 

ARMSTRONG,  H.  E.  The  Teaching  of  the  Scientific  Method.  2d, 
ed.  New  York,  Macmillan,  1910. 

JAMES,  WILLIAM.  Talks  to  Teachers  on  Psychology.  New  York,. 
Holt,  1907.  -j 

McMuRRY,  C.  A.  Special  Method  in  Elementary  Science.  New 
York,  Macmillan,  1904. 

FREY,  O.  Physikalische  Arbeitsunterricht.  Leipzig,  Wunderlich, 
1907. 

SCHMID,  B.  Die  Naturwissenschaftliche  Unterricht,  Leipzig, 
Teubner,  1907. 

PERRY,  J.    England's  Neglect  of  Science.    London,  Unwin,  1900. 

DUHEM,  P.  Traite  d'Energetique  on  de  Thermodynamique  generate. 
2  vols.  Paris,  Sauthier  Villars,  1911. 

School  Science  and  Mathematics.  This  journal  contains  many  ex- 
cellent articles  on  practical  methods  of  teaching  physics. 
Published  by  Smith  &  Turton,  2059  East  72d  Place,  Chicago. 


CHAPTER  XI 
THE  LABORATORY  WORK 

108.  Current  Ideas  of  Laboratory  Work. — The  ideas 
that  were  prominent  when  laboratory  work  in  physics 
began  to  be  introduced  into  the  schools  have  been  treated 
in  Chapter  III.  The  demand  for  individual  work  by 
the  pupils  was  the  outgrowth  of  the  general  demand  for 
object  teaching.  Since  "  seeing  is  believing,"  the  chil- 
dren should  see  for  themselves  that  the  "  facts  and  laws 
of  elementary  physics  "  were  actually  what  they  were 
supposed  to  be,  namely,  "  true."  The  fundamental 
idea  was  that  the  actual  handling  of  the  apparatus  and 
the  making  of  the  measurements  would  make  the  law 
more  real  and  concrete  to  the  pupil;  and,  therefore, 
that  he  would  be  able  to  grasp  its  meaning  better  and  to 
apply  it  with  greater  intelligence. 

That  this  idea  is  perfectly  true,  whenever  the  state- 
ment just  made  correctly  describes  the  actual  work  done, 
no  one  will  for  one  minute  deny.  Whenever  the  labora- 
tory work  is  so  conducted  as  to  make  a  thing  concrete 
to  the  pupil,  the  desired  result  follows.  This  was  un- 
doubtedly the  case  with  much  of  the  work  done  under  the 

246 


THE  LABORATORY  WORK  247 

guidance  of  books  like  that  of  Gage.  Most  of  the  ex- 
periments which  he  uses  are  well  calculated  to  render 
the  ideas  that  they  exemplify  concrete  to  the  pupils. 

But  as  the  high  school  physics  became  universityized 
and  as  the  laboratory  facilities  increased  and  equipment 
became  more  plentiful,  the  experiments  became  more 
elaborate,  more  accurate,  and,  what  was  worse,  more 
abstract.  Thus  the  Harvard  Descriptive  List  in  1886 
was  designed :  "  ist,  to  train  the  young  student  by  means 
of  tangible  problems  requiring  him  to  observe  accurately, 
to  attend  strictly,  and  to  think  clearly;  2d,  to  give 
practice  in  the  methods  by  which  physical  facts  and 
laws  are  discovered;  3d,  to  give  practical  acquaintance 
with  a  considerable  number  of  these  facts  and  laws,  with 
a  view  to  their  utility  in  the  thought  and  actions  of 
educated  men."  1  In  1897  the  statement  of  the  Har- 
vard laboratory  requirement  read : 2  "  The  pupil's 
laboratory  work  should  give  practice  in  the  observation 
and  explanation  of  physical  phenomena,  some  familiarity 
with  methods  of  measurement,  and  some  training  of 
the  hand  and  the  eye  in  the  direction  of  precision  and 
skill.  It  should  also  be  regarded  as  a  means  of  fixing  in 
the  mind  of  the  pupil  a  considerable  variety  of  facts  and 
principles."  Again,  after  discussing  the  experiment 

1  Ante,  p.  54. 

2  Smith  &  Hall,  Teaching  of  Chemistry  and  Physics,  p.  272. 


248  THE  TEACHING  OF  PHYSICS 

with  the  parallelogram  of  forces,  Professor  Hall  says : 1 
11  The  object  of  the  experiment  in  this  case  is  to  make 
the  pupil  realize  the  meaning  of  the  law,  while  giving 
him  an  opportunity  to  exercise,  and  by  the  final  result 
to  test,  his  skill." 

It  will  be  noted  that  the  idea  of  "  utility  in  the  thought 
and  actions  of  educated  men  "  has  disappeared,  and  in 
its  place  the  pupil  is  given  a  chance  to  "  test  his  skill  " 
in  making  accurate  measurements  and  to  "  realize  the 
meaning  of  the  law."  It  will  also  be  noted  that  the 
first  purpose  was  "  to  train  the  young  student  to  observe 
accurately  and  to  think  clearly." 

The  latest  expression  of  opinion  on  this  subject  comes 
from  Coleman,  in  his  essay  on  the  Purpose  and  Method 
of  Experimental  Work  in  Physics.2  The  purpose  of 
the  work  is  thus  set  forth :  "Its  specific  purpose  is  to 
enlarge  the  pupil's  acquaintance  with  the  facts  of  the 
subject  at  first  hand.  .  .  .  The  laboratory  experiment 
is  not  a  proof  of  the  law,  but  an  aid  to  the  right  under- 
standing of  it.  ...  If  it  has  only  such  connection  with 
the  work  of  the  classroom  as  the  pupil  makes  on  his 
own  initiative,  it  will  have  very  little  value  indeed.  .  .  . 
The  text  and  the  experiments  are  different  lines  of  ap- 

1  Smith  &  Hall,  I.e.,  p.  279. 

2  Coleman,  School  Science  and   Mathematics,   Vol.  XI,  p.  816,  De- 
cember, 1 91 1. 


THE  LABORATORY  WORK  249 

proach  to  the  same  goal,  namely,  an  understanding  of 
physics.  ...  It  is  the  business  of  the  elementary  labo- 
ratory to  afford  opportunity  for  gaining  a  selected  and 
directed  experience  under  good  working  conditions.  .  .  . 
The  laboratory  experiment  is  predetermined  and  fixed. 
It  follows  a  set  of  written  or  printed  directions,  from 
which  the  pupil  can  rarely  depart  with  any  profitable 
result." 

This  statement  of  the  case  gives  the  present  generally 
prevailing  ideas  of  the  use  of  the  laboratory  work.  In 
brief,  the  laboratory  is  the  place  where  the  students 
get  predetermined  experiences,  cunningly  devised  to 
make  the  law  intelligible  to  them  and  to  help  them  to 
keep  it  in  mind ;  to  the  end  that  they  may  "  understand 
physics." 

109.  Current  Ideas  are  Inadequate.  —  This  purpose 
of  the  laboratory  work  is  so  generally  accepted  that 
there  can  be  little  doubt  that  it  is  correct  as  far  as  it  goes. 
In  the  light  of  the  discussions  of  the  previous  chapters, 
we  may  very  reasonably  question  its  adequacy.  Is  that 
all  the  laboratory  work  is  for  ?  If  so,  is  the  game  worth 
the  candle?  Is  the  "  understanding  of  physics  "  which 
the  pupils  actually  get  from  it  worth  the  time  and  labor 
and  expense  required  by  the  work?  If  we  grant  that 
some  pupils  gain  an  understanding  of  physics  because 
of  it,  we  must  also  grant  that  many  more  do  not  do  this. 


250  THE  TEACHING  OF  PHYSICS 

And  anyway,  an  understanding  is  an  intellectual  thing, 
while  in  ideals  of  method  —  which  are  the  transferable 
factors  —  the  emotional  elements  are  by  far  the  most 
important.  What  is  the  emotional  reaction  of  the  ma- 
jnriiynfJjifL^"]}i^^  those jwhoJakejjtasigs  and 

those  who  avoid  it?  Why  do  they  call  the  experiments 
" "  stunts  "r~ Why  do  they  aim  at  the  "  correct  "  results, 
predetermined  and  fixed,  instead  of  at  useful  experience? 

The  answers  to  these  questions  are  not  hard  to  find. 
Few  pupils  really  want  to  know  the  facts  and  laws  that 
the  experiments  are  devised  to  make  clear  to  them.  And 
why  should  they,  when  the  uses  of  these  are  not  explained 
until  the  law  is  "understood"?  Unless  the  prob- 
lem which  they  are  trying  to  solve  has  been  defined  from 
a  forked-road  situation  that  is  significant  to  the  pupils, 
thinking  does  not  begin;  and  the  experiment  that  is 
attempted  before  it  is  thus  justified  in  advance,  or  be- 
fore a  need  for  it  is  felt,  is  of  little  real  educative  value. 
Little  attention  has  as  yet  been  given  to  organizing  a 
course  in  such  a  way  that  the  laboratory  experiments 
become  necessary,  not  to  illustrate  a  principle,  but  to 
furnish  information  that  is  needed  in  order  to  solve  some 
problem  whose  solution  the  pupils  desire  to  find. 

no.  The  Result  should  be  Significant.  —  Why  should 
not  the  elementary  laboratory  be  related  to  the  ele- 
mentary study  of  physics  very  much  as  the  advanced 


THE  LABORATORY  WORK  251 

laboratory  is  to  the  advanced  study  of  physics?  No 
research  student  in  physics  ever  makes  an  experiment 
just  to  "  see  the  wheels  go  round  "  and  have  a  fact  made 
concrete.  He  goes  to  the  laboratory  for  information 
which  he  cannot  get  elsewhere.  He  has  a  problem 
whose  solution  he  is  seeking  under  the  impulse  of  mo- 
tives of  his  own,  and  he  needs  information  which  the 
laboratory  alone  can  supply  in  order  to  solve  it.  He 
does  not  know  the  result  in  advance,  else  there  would 
be  no  need  for  the  laboratory  work.  He  does  not  have 
a  cut-and-dried,  predetermined  experiment,  with  de- 
tailed directions  for  its  manipulation. 

With  these  points  well  in  mind,  turn  back  to  the 
Harvard  Descriptive  List  (p.  56),  which  has  been  the 
model  of  most  of  the  laboratory  lists  and  manuals  since. 
Consider  any  of  the  topics  in  that  list :  breaking  strength 
of  a  wire,  elasticity,  bending,  coefficient  of  friction, 
specific  gravity  of  a  solid  that  will  sink  in  water,  com- 
parison of  masses,  and  ask  yourself  whether,  if  you  were 
a  high  school  pupil  again,  you  would  glow  with  eager 
enthusiasm  to  know  the  results  of  any  of  these  experi- 
ments for  the  mere  sake  of  the  knowledge.  Why  should 
the  pupil  be  keen  to  know  the  breaking  strength  of  a 
wire,  or  the  coefficient  of  friction  between  a  block  of  wood 
and  a  board?  To  what  inherent  need  of  his  does  the 
experiment  minister? 


252  THE  TEACHING  OF  PHYSICS 

Or  again,  take  any  laboratory  manual  and  open  it  at 
random ;  read  the  experiment  through,  and  ask  yourself 
why  a  pupil  should  be  enthusiastic  over  it  or  should  even 
want  to  know  the  result.  There  is  no  answer  to  this 
question,  —  unless  it  be  that  he  shouldn't.  The  experi- 
ments are  not  designed  to  furnish  information  that  the 
pupil  needs  in  order  to  solve  a  problem  that  is  significant 
to  him.  They  are  designed  simply  and  solely  to  furnish 
a  concrete  basis  for  his  appreciation  of  some  tidbit  of 
physics.  He  must  go  through  the  motions  indicated, 
not  to  satisfy  his  spirit  of  wonder,  but  to  fulfill  to  the 
letter  some  "  requirement  "  of  the  school  system.  The 
process  is  somewhat  like  compelling  a  hungry  boy  to 
stuff  his  blouse  with  apples  in  order  to  make  him  appear 
plump  and  hearty,  instead  of  letting  him  eat  them. 

For  example,  on  opening  a  book  at  random,  the  fol- 
lowing appears :  "  To  study  the  effect  of  change  of 
pressure  on  the  volume  of  a  gas,  or  to  verify  Boyle's 
law."  Then  follows  the  usual  description  of  apparatus, 
procedure,  discussion.  This  latter  consists  of  the  fol- 
lowing information,  dear  to  the  hearts  of  the  pupils, 
and  well  calculated  to  inspire  them  with  reverence  for 
the  methods  of  science :  "  It  is  a  law  of  mathematics 
that  when  the  product  of  two  variables  (sic  /)  is  constant, 
the  two  quantities  are  inversely  proportional.  Is  the 
product  P  X  V  constant,  at  least  as  far  as  the  sure 


THE  LABORATORY  WORK  253 

figures?  Another  way  to  consider  this  is  to  notice 
whether  the  pressure  is  one  half  as  great  as  at  first,  when 
the  volume  is  two  times  as  great ;  one  third  as  great 
when  the  volume  is  three  times  as  great,  etc."  In- 
teresting, no  doubt,  and  valuable  as  physics ;  but  what 
problem  in  life  does  it  help  him  to  solve  ? 

The  result  of  this  sort  of  work  is  thus  described  by 
Poincare : l  "  There  is  one  thing  that  strikes  me :  it  is 
how  many  young  people  who  have  received  a  high  school 
training  are  far  from  being  able  to  apply  the  mechanical 
laws  that  have  been  taught  them  to  the  real  world.  It 
is  not  that  they  are  incapable  of  doing  this ;  they  never 
think  of  it.  For  them  the  world  of  science  and  that  of 
reality  are  separated  by  a  yawning  chasm.  It  is  not 
rare  to  see  a  well-to-do  man,  probably  a  bachelor,  riding 
in  a  carriage  and  imagining  that  he  is  helping  it  to  go  by 
pushing  forward  on  the  floor,  notwithstanding  the  fact 
that  this  shows  a  failure  to  apprehend  the  principle  of 
action  and  reaction." 

in.  The  Real  Purpose.  —  The  real  purpose  of  the 
laboratory  and  the  inadequacy  of  the  idea  that  it  is  the 
place  to  render  ideas  concrete  merely  by  presenting  a 
series  of  ingeniously  devised  objects  is  thus  pointed  out 
by  Dewey : 2  "  Since  the  concrete  denotes  anything  ap- 

1  Poincar6,  Science  et  Mithode,  p.  146. 

2  Dewey,  How  We  Think,  pp.  139  sq. 


254  THE  TEACHING  OF  PHYSICS 

plied  to  activities  for  the  sake  of  dealing  effectively 
with  the  difficulties  that  present  themselves  practically, 
'  beginning  with  the  concrete  '  signifies  that  we  should 
at  the  outset  make  much  of  doing;  especially,  make 
much  in  occupations  that  are  not  of  a  routine  and  me- 
chanical kind  and  hence  require  intelligent  selection  and 
adaptation  of  means  and  materials.  We  do  not  '  follow 
the  order  of  nature '  when  we  multiply  mere  sensations 
or  accumulate  physical  objects.  If  physical  things  used 
in  teaching  number  or  geography  or  anything  else  do 
not  leave  the  mind  illuminated  with  recognition  of  a 
meaning  beyond  themselves,  the  instruction  that  uses 
them  is  as  abstract  as  that  which  doles  out  ready-made 
definitions  and  rules;  for  it  distracts  attention  from 
ideas  to  mere  physical  excitations. 

"  The  conception  that  we  have  only  to  put  before  the 
senses  particular  physical  objects  to  impress  certain 
ideas  upon  the  mind  amounts  almost  to  a  superstition. 
The  introduction  of  object  lessons  and  sense  training 
scored  a  distinct  advance  over  the  prior  method  of  lin- 
guistic symbols,  and  this  advance  tended  to  blind  edu- 
cators to  the  fact  that  only  a  halfway  step  had  been 
taken.  Things  and  sensations  develop  the  child,  indeed, 
but  only  because  he  uses  them  in  mastering  his  body 
and  in  the  scheme  of  his  activities.  Appropriate  con- 
tinuous occupations  or  activities  involve  the  use  of 


THE  LABORATORY  WORK  255 

natural  materials,  tools,  modes  of  energy,  and  do  it  in  a 
way  that  compels  thinking  as  to  what  they  mean,  how 
they  are  related  to  one  another,  and  to  the  realization  of 
ends;  while  the  mere  isolated  presentation  of  things 
remains  barren  and  dead.  A  few  generations  ago  the 
great  obstacle  in  the  way  of  reform  of  primary  education 
was  belief  in  the  almost  magical  efficacy  of  the  symbols 
of  language  (including  number)  to  produce  mental  train- 
ing ;  at  present,  belief  in  the  efficacy  of  objects  just  as 
objects,  blocks  the  way.  As  frequently  happens,  the 
better  is  an  enemy  of  the  best." 

112.  Conditions  for  Vital  Work.  —  Since  the  current 
forms  of  laboratory  practice  are  inadequate  to  achieve 
the  purposes  of  physics  teaching,  as  set  forth  in  Chapter 
IX,  what  kind  of  work  would  be  more  profitable?  If 
we  recall  the  conditions  under  which  the  specific  dis- 
cipline of  physics  may  be  made  general,  it  will  not  be 
difficult  to  reorganize  the  work  without  throwing  away 
entirely  the  equipment  which  the  laboratories  already 
have  for  their  supposed  purpose  of  "  fixing  in  mind  the 
facts  and  laws  of  elementary  physics."  The  conditions  ^ 
to  be  fulfilled  are  these:  (i)  An  ambiguous  or  forked- 
road  situation  must  be  produced  in  which  thinking  be- 
gins and  which  leads  to  the  definition  of  a  problem  signifi- 
cant to  the  pupil.  (2)  The  problem  must  be  of  such  a 
nature  that  its  answer  cannot  be  obtained  without 


256  THE  TEACHING  OF  PHYSICS 

making  measurements  or  at  least  experiments  in  the 
laboratory. 

113.  Suitable  Problems.  —  It  is  not  difficult  to  meet 
these  conditions,  once  the  teacher's  mind  is  freed  from 
the  incubus  of  the  "  facts  and  laws  of  elementary  phys- 
ics "  as  set  forth  in  lists  backed  by  the  "  authority  of 
official  utterance."  Since  the  first  problems  must  of 
necessity  arise  from  the  pupil's  daily  experiences,  they 
will  be  different  in  different  localities.  As  samples  of 
the  kind  of  problems  that  may  be  used  to  advantage 
in  fulfillment  of  the  conditions  stated,  the  following  list 
is  appended  as  suitable  for  use  with  the  topics  treated 
in  the  last  chapter.  This  is  not  the  only  possible  list; 
an  infinite  number  of  others  are  equally  possible  and 
perhaps  far  better.  It  is  added  simply  to  suggest  the 
kind  of  problem  that  may  prove  adequate. 

1.  Does  it  require  more  work  to  slide  a  cake  of  ice 
up  an  inclined  plane  than  it  does  to  lift  it  vertically 
through  the  same  height  ?    If  so,  how  much  more  ? 

2.  How  can  you  alter  the  inclined  plane  to  increase 
its  efficiency  ? 

3.  Can  the  ice  be  lifted  into  the  ice  house  more  effi- 
ciently with  a  set  of  pulleys  than  with  an  inclined  plane  ? 

4.  Does  it  require  more  work  to  lift  a  stone  with  a 
crowbar  than  to  raise  it  by  hand  through  the  same 
height?    How  much  more? 


THE  LABORATORY  WORK  257 

5.  Is  a  wheel  and  axle  more  efficient  than  a  set  of  pul- 
leys for  hauling  water  from  a  well  ?    How  much  more  ? 

6.  Is  a  force  pump  more  efficient  than  a  lift  pump? 
How  much  ? 

7.  Which  of  two  water  motors  is  the  more  efficient? 
How  much  more?    Does  the  efficiency  of  the  motor 
depend  on  the  speed  or  on  the  load?    What  are  the 
conditions  of  maximum  efficiency? 

8.  Is  a  given  motor  more  efficient  on  a  tap  in  the  base- 
ment than  on  one  on  the  third  floor?    Is  there  any  re- 
lation between  pressure  and  efficiency? 

9.  Which  is  the  most  efficient  gas  burner,  a  Bunsen 
burner  or  one  from  a  gas  stove? 

10.  With  a  given  burner,  which  kind  of  kettle  is  most 
efficient :  one  of  iron,  one  of  tin,  one  of  enameled  ware, 
or  one  of  aluminum?    How  much  more? 

11.  Does  a  given  kettle  containing  a  given  quantity 
of  water  at  tap  temperature  come  to  a  boil  in  less  time 
when  the  cover  is  off  than  it  does  when  the  cover  is  on  ? 
How  much  more  ? 

12.  If  it  takes  fifteen  minutes  for  an  uncovered  kettle 
containing  one  kilogram  of  water  at  tap  temperature  to 
come  to  a  boil,  how  much  water  will  boil  away  in  five 
minutes?    From  the  data  obtained  compute  the  heat 
vaporization  of  water.     Correct  the  result  with  the  data 
obtained  in  problem  11. 


258  THE  TEACHING  OF  PHYSICS 

13.  Is  the  heat  equivalent  of  the  city  gas  up  to  stand- 
ard (600  B.  T.  U.  per  cubic  foot)  ? 

14.  Which  kind  of  coal  in  your  town  gives  the  greatest 
number  of  heat  units  per  pound  ? 

15.  Is  it  cheaper  to  distill  water  with  a  laboratory 
still,  burning  gas  at  eighty  cents  per  thousand  cubic 
feet,  or  to  buy  distilled  water  from  the  druggist  at  ten 
cents  a  gallon  ?    How  much  cheaper  ? 

1 6.  What  is  the  thermal  efficiency  of  the  laboratory 
still?    How  can  it  be  increased? 

17.  Which  radiates  more  heat  per  watt  hour,  a  car- 
bon or  a  tungsten  lamp?    How  much? 

1 8.  Which  of  two  small  electric  motors  is  the  more 
efficient?    How  much  more?    Does  the  efficiency  de- 
pend on  the  speed  or  on  the  load  ? 

19.  What  is  the  efficiency  of  a  small  gas  or  gasoline 
engine? 

20.  Which  costs  less  per  horse-power  hour:  the  water 
motor,  the  electric  motor,  or  the  gas  engine  that  you 
have  tested?    How  much? 

As  samples  of  the  kind  of  laboratory  problems  that 
may  prove  faithful  in  connection  with  the  example  of  a 
method  of  treating  optics  and  light,  consider  the  fol- 
lowing :  — 

21.  Of  two  pinhole  cameras  of  the  same  size,  which 
makes  the  clearest  picture,  one  with  a  hole  one  milli- 


THE  LABORATORY  WORK  259 

meter  in  diameter  or  one  with  a  hole  two  millimeters  in 
diameter  ? 

22.  Do  different-sized  cameras  when  pointed  from  a 
given  place  at  the  same  object  all  give  images  of  the  same 
size  ?    Is  there  any  relation  between  the  size  of  the  image 
and  the  distance  from  the  center  of  the  lens  to  the  ground 
glass  ? 

23.  Can  you   construct  a   telescope  with   spectacle 
lenses?    How?    What  is  its  magnification? 

24.  Are  the  object  and  image  formed  by  a  lens  closer 
together  when  both  are  of  the  same  size  than  when  one 
is  larger  than  the  other  ? 

25.  Is  there  any  relation  between  distance  between 
object  and  image,  when  both  are  of  the  same  size,  and 
the  principal  focal  length  of  the  lens? 

26.  Does  it  cost  more  per  hour  to  light  a  room  to  a 
given  brightness  with  candles  or  with  oil? 

27.  Which   gives   the   most  light  per  watt  hour,  a 
carbon-filament   lamp,  or  one   with  a  tungsten   or   a 
tantalum  filament?    How  much  more? 

28.  In  your  town  is  it  cheaper  to  light  houses  by 
electricity  or  by  gas  ?    How  much  ? 

29.  How  much  more  efficient  is  a  Welsbach  burner 
than  an  ordinary  fish-tail  gas  burner  ? 

30.  Is  an  electric  arc  lamp  more  efficient  than  a 
tungsten  lamp?    How  much  more? 


26o  THE  TEACHING  OF  PHYSICS 

Since  there  are  no  laboratory  manuals  written  on  the 
basis  here  indicated,  the  following  experiments  are  sug- 
gested as  typical  of  the  kind  of  problem  that  may  be 
found  useful  in  connection  with  other  topics  than  those 
discussed. 

31.  Five  cubic  feet  of  lead  are  used  to  make  the  keel 
of  a  boat.     How  much  does  the  lead  weigh  out  of  water  ? 
Does  it  sink  the  boat  as  far  when  it  is  fastened  to  the 
keel  under  water  as  it  does  when  placed  inside  the  boat? 

32.  What  is  the  specific  gravity  of  the  milk  furnished 
by  your  milkman?    Is  it  up  to  standard? 

33.  How  many  cubic  feet  of  pine  are  required  to 
make  a  raft  that  would  float  a  one  hundred  pound  boy 
out  of  water? 

34.  Which  weighs   more,   a   concrete   house   or   the 
same  house  built  of  brick  ?    How  much  more  ? 

35.  Does  the  consumer  get  more  gas  for  his  money 
when  the  pressure  on  the  mains  is  high  than  when  it  is 
low? 

36.  How  much  ice  is  melted  in  a  refrigerator  when  a 
quart  of  milk  at  a  temperature  of  20°  C.  is  placed  in  the 
refrigerator  and  cooled  to  2°  C.  ? 

37.  How  great  is  the  difference  in  pressure  between 
a  water  tap  on  the  first  floor  and  one  on  the  third  floor  ? 
What  is  the  difference  in  level?     Is  the  difference  the 
same  whether  one  tap  is  directly  over  the  other  or  not  ? 


THE  LABORATORY  WORK  261 

38.  What  is  the  velocity  of  water  flowing  through  a 
nozzle  one  quarter  inch  in  diameter  under  a  pressure  of 
twenty  pounds  to  the  square  inch? 

39.  What  is  the  efficiency  of  this  hydraulic  ram? 

40.  What  is  the  dew  point  to-day? 

41.  Which  makes  the  best  lining  for  a  fireless  cooker, 
an  air  space,  felt,  excelsior,  mineral  wool,  or  granulated 
cork?    Are  any  of  these  as  good  as  that  of  the  thermos 
bottle? 

42.  How  is  the  siren  whistle  constructed,  and  why 
does  it  produce  its  peculiar  effect? 

43.  How  long  is  the  sound  wave  of  your  own  voice? 

44.  Why  is  your  image  in  a  plane  mirror  reversed  ? 

45.  What  makes  the  "  cow's  hoof  "  in  a  glass  half-full 
of  milk  when  it  is  placed  below  and  to  one  side  of  a 
candle  ? 

46.  How  do  luxifer  prisms  and  holophane  shades  help 
to  light  up  dark  rooms?    Why  is  there  no  color  in  the 
light  transmitted  by  them? 

47.  Which  of  two  electric  toasters  or  curling  irons  is 
the  most  efficient  ?    How  much  more  ? 

48.  Which  form  of  voltaic  cell  is  best  for  doorbells? 
Which  for  telegraph  lines?    Which  for  toy  motors? 

49.  Which  is  the  best  dry  cell  on  the  market? 

50.  Which  is  the  best  kind  of  wire  to  use  in  making 
electric  toasters? 


262  THE  TEACHING  OF  PHYSICS 

51.  Is  the  resistance  of  an  incandescent  lamp  greater 
when  it  is  hot  than  when  it  is  cold  ?  How  much  greater  ? 

The  foregoing  list  is  not  to  be  taken  as  a  syllabus  of 
experiments  for  a  laboratory  course.  It  is  merely  sug- 
gestive of  the  type  of  experimental  problem  which  seems 
well  adapted  to  the  working  hypotheses  of  democratic 
education.  The  specific  problems  used  must  be  different 
in  different  localities  because  the  local  surroundings  are 
different.  Each  teacher  will  have  no  difficulty  in  finding 
plenty  of  problems  pf  this  kind  in  his  immediate  envi- 
ronment if  he  will  but  remove  from  his  eyes  the  bandage 
of  prescribed  physics  which  was  described  in  Chapter  III. 

114.  Engineering  or  Physics  ?  —  Objection  will  doubt- 
less be  raised  to  this  type  of  experiment  on  the  ground 
that  it  is  engineering  and  not  physics.  This  objection 
is  perfectly  valid,  as  stated  before,  when  the  work  is  of 
such  a  kind  as  to  justify  the  statement  that  it  is  engi- 
neering and  not  physics.  Nevertheless,  this  type  of  work, 
even  though  it  stops  at  the  engineering  stage,  is  vastly 
more  valuable  as  a  means  to  general  education  than  is 
pure  physics  of  the  kind  specified  by  college  entrance 
syllabi  and  examinations.  For  this  work,  by  beginning 
with  problems  of  the  daily  life,  makes  possible  a  motiva- 
tion without  which  the  training  given  is  not  likely  to  be 
of  the  transferable  kind.  A  transferable  ideal  of  the 
scientific  method  of  solving  problems  is  of  far  more  value 


THE  LABORATORY  WORK  263 

in  after  life  to  the  great  majority  of  the  pupils  than  is  a 
knowledge  of  the  facts  and  laws  of  elementary  physics, 

But  whether  this  type  of  work  stops  at  the  engineering 
stage  or  not  depends  entirely  on  the  skill  and  ability  of 
the  teacher.  When  he  has  once  secured  the  attention 
of  the  pupils  by  means  of  significant  problems  from  the 
daily  life,  it  is  possible  to  make  the  more  and  more  ab- 
stract and  remote  problems  of  physics  significant  and 
hence  capable  of  giving  transferable  training.  The 
converse  is,  however,  seldom  true.  All  teachers  are 
constantly  amazed  at  the  inability  of  the  pupils  to 
"  apply  "  their  pure  physics  even  to  the  physical  prob- 
lems of  their  daily  life,  to  say  nothing  of  their  inability 
to  think  scientifically  on  problems  outside  of  physics. 
No  such  difficulties  appear  in  schools  in  which  the  en- 
gineering approach  is  used  effectively;  as  in  the  Lewis 
Institute  in  Chicago,  the  High  School  at  Menomonie, 
Wis.,  the  Industrial  High  School  at  New  Bedford, 
Mass.,  the  Ethical  Culture  School  in  New  York,  and  the 
Technical  High  School  in  Cleveland,  Ohio. 

115.  Go  from  Concrete  to  Abstract.  —  The  principles 
that  should  guide  the  teacher  in  planning  and  conducting 
his  laboratory  work  have  been  thus  stated  by  Dewey : l 
"The  interest  in  results,  in  the  successful  carrying  on  of 
an  activity,  should  be  gradually  transferred  to  the  study 

1  Dewey,  How  We  Think,  p.  140. 


264  THE  TEACHING  OF  PHYSICS 

of  objects  —  their  properties,  consequences,  structures, 
causes,  and  effects.  The  educative  activities  of  childhood 
should  be  so  arranged  that  direct  interest  in  the  activity 
and  its  outcome  create  a  demand  for  attention  to  matters 
that  have  a  more  and  more  indirect  and  remote  con- 
nection with  the  original  activity.  The  direct  interest 
in  carpentering  or  shop  work  should  yield  organically 
and  gradually  to  an  interest  in  geometric  and  mechanical 
problems.  The  interest  in  cooking  should  grow  into  an 
interest  in  chemical  experimentation  and  in  physiology 
and  hygiene  of  bodily  growth.  This  development  is  what 
the  term  go  signifies  in  the  maxim  '  go  from  the  concrete 
to  the  abstract ' ;  it  represents  the  dynamic  and  truly 
educative  factor  of  the  process. 

"  The  outcome,  the  abstract  to  which  education  is  to 
proceed,  is  an  interest  in  intellectual  matters  for  their 
own  sake,  a  delight  in  thinking  for  the  sake  of  thinking. 
It  is  an  old  story  that  acts  and  processes  which  at  the 
outset  are  incidental  to  something  else  develop  and 
maintain  an  absorbing  value  of  their  own.  So  it  is  with 
thinking  and  with  knowledge ;  at  first  incidental  to  re- 
sults and  adjustments  beyond  themselves,  they  attract 
more  and  more  attention  to  themselves,  till  they  become 
ends,  not  means. 

"  Abstract  thinking,  it  should  be  noted,  represents  an 
end,  not  the  end.  The  power  of  sustained  thinking  on 


THE  LABORATORY  WORK  265 

matters  remote  from  direct  use  is  an  outgrowth  of  prac- 
tical and  immediate  modes  of  thought,  but  not  a  sub- 
stitute for  them.  The  educational  end  is  not  the  destruc- 
tion of  power  to  think  so  as  to  surmount  obstacles  and 
adjust  means  and  ends;  it  is  not  its  replacement  by 
abstract  reflection.  Nor  is  theoretical  thinking  a  higher 
type  of  thinking  than  practical.  A  person  who  has  at 
command  both  types  of  thinking  is  of  a  higher  order  than 
he  who  possesses  only  one.  Methods  that  in  developing 
abstract  intellectual  abilities  weaken  habits  of  practical 
or  concrete  thinking  fall  as  much  short  of  the  educational 
ideal  as  do  the  methods  that  in  cultivating  ability  to 
plan,  to  invent,  to  arrange,  to  forecast,  fail  to  secure 
some  delight  in  thinking,  irrespective  of  practical  con- 
sequences. 

"  Educators  should  also  note  the  very  great  individual 
differences  that  exist;  they  should  not  try  to  force  one 
pattern  and  model  upon  all.  In  many  (probably  the 
majority)  the  executive  tendency,  the  habit  of  mind  that 
thinks  for  purposes  of  conduct  and  achievement,  not  for 
the  sake  of  knowing,  remains  dominant  to  the  end. 
Engineers,  lawyers,  doctors,  merchants,  are  much  more 
numerous  in  adult  life  than  scholars,  scientists,  and 
philosophers.  While  education  would  strive  to  make 
men  who,  however  prominent  their  professional  interests 
and  aims,  partake  of  the  spirit  of  the  scholar,  philosopher, 


266  THE  TEACHING  OF  PHYSICS 

and  scientist,  no  good  reason  appears  why  education 
should  esteem  the  one  mental  habit  inherently  superior 
to  the  other,  and  deliberately  try  to  transform  the  type 
from  practical  to  theoretical.  Have  not  our  schools  been 
one-sidedly  devoted  to  the  more  abstract  type  of  think- 
ing, thus  doing  injustice  to  the  majority  of  the  pupils? 
Has  not  the  idea  of  a  '  liberal '  and  '  humane '  educa- 
tion tended  too  often  in  practice  to  the  production  of 
technical,  because  overspecialized,  thinkers?  " 

1 1 6.  The  Psychological  and  the  Logical.  —  Examples 
of  one  way  of  doing  this  have  been  given  in  the  last  chap- 
ter. It  was  there  shown  how  the  doctrine  of  energy 
might  be  reached  in  a  course  that  began  with  studies  of 
sliding  ice  into  an  ice  house,  of  the  efficiencies  of  water 
motors,  teakettles,  steam  engines,  electric  motors  and 
heaters,  and  the  like.  In  like  manner  the  optics  began 
with  a  discussion  of  the  apparent  sizes  of  everyday  ob- 
jects and  led  on  to  the  principles  of  focal  length  and  op- 
tical instruments.  It  need  not  stop  here,  if  the  teacher 
deems  it  wise  to  continue  on  into  interference,  diffraction, 
and  resolution. 

The  study  of  the  fireless  cooker  has  been  denounced  as 
devoid  of  pure  physics.  But  even  this  useful  device, 
besides  leading  to  the  ideas  of  conduction  and  convec- 
tion, may  furnish  a  useful  starting  point  for  a  study 
of  the  relations  of  emission,  reflection,  and  absorption. 


THE  LABORATORY  WORK  267 

Does  it  improve  the  efficiency  of  the  cooker  to  paint  it 
black  inside  or  to  have  polished  vessels  and  linings? 
The  important  things  are  that  the  problems  chosen  should 
be  such  that  the  pupils  want  to  know  the  results,  and 
that  the  experiment  is  necessary  to  get  the  answers. 
Starting  on  such  a  significant  basis,  the  foundations  are 
laid  in  concrete,  and  on  such  a  foundation  a  larger  and 
finer  superstructure  can  be  reared  than  is  possible,  as 
is  now  too  often  the  case,  when  we  attempt  to  build  the 
cupolas  and  the  dome  first,  trusting  that  the  concrete 
foundations  will  supply  themselves  somehow. 

It  is  important  to  note  that  the  method  here  advocated 
is  the  direct  converse  of  that  generally  in  use  at  present. 
The  present  logical  method  proceeds  in  the  order: 
principle,  demonstration,  exemplification  in  laboratory, 
application.  In  the  new  psychological  method  the  order 
is:  application,  problem,  solution  in  the  laboratory, 
principle.  To  those  who  insist  that  there  is  no  distinc- 
tion between  the  logical  and  the  psychological  orders, 
this  statement  of  the  case  is  recommended  for  considera- 
tion. 

A.     The  fundamental  distinction  between  the  logical  and 
the  psychological  is  thus  stated  by  Dewey : 1   "All  in- 
tellectual activity  is  directed  towards  an  end.    The  end, 
therefore,  exists  in  the  mind  by  way  of  feeling.    We  do 
1  Dewey,  Psychology,  p.  396. 


268  THE  TEACHING  OF  PHYSICS 

not  know  what  it  is,  but  we  dimly  feel  what  it  is ;  and  we 
select  material  that  feels  congruous  with  this  end,  and 
reject  that  which  feels  inharmonious.  The  direction  of 
all  intellectual  processes  by  feeling  is  very  commonly 
overlooked,  but  it  is  fundamental.  .  .  .  This  foregrasp 
of  feeling  upon  what  is  not  yet  intellectually  identified 
and  discriminated  constitutes  a  form  of  intuition.  It  is 
a  matter  that  cannot  be  subjected  to  rules.  After, 
however,  the  end  has  been  reached,  it  is  possible  for 
consciousness  reflectively  to  trace  the  steps  and  formu- 
late the  process.  Feeling,  when  thus  reflectively  criti- 
cised and  crystallized  into  intellectual  propositions,  gives 
rise  to  the  rules  of  the  logic  of  method.  Logic,  as  the 
science  of  investigation,  must  wait  upon  the  actual  dis- 
coveries of  the  intellect,  which  are  controlled  by  feeling. 
It  is  reflective  and  critical,  not  intuitive  and  creative; 
it,  therefore,  may  be  taught,  while  the  actual  process  of 
discovering  new  truth  can  never  be  imparted.  It  must 
follow  after,  not  precede  discovery.  Logic,  in  short, 
only  generalizes  and  crystallizes  what  was  originally 
existing  in  the  form  of  feeling." 

Though  Platonic  thought  and  the  doctrine  of  formal 
discipline  may  have  proved  adequate  to  guide  the  aris- 
tocratic schooling  of  the  past,  they  are  clearly  inadequate 
to  control  the  democratic  education  of  the  present  and 
the  future.  The  chief  reason  for  this  is  that  both  ignore 


THE  LABORATORY  WORK  269 

the  functions  of  the  feelings  and  emotions  in  all  really 
educative  processes.  In  like  manner  the  laboratory 
work  in  Physics  becomes  Platonic  and  formal  when  it 
strives  merely  to  fix  in  the  mind  of  the  pupil  the  facts 
and  laws  of  elementary  physics  as  purely  intellectual 
propositions.  This  process  may  lead  to  preparation  for 
the  career  of  a  physicist,  but  it  touches  only  slightly  the 
lives  of  most  of  the  pupils.  It  is,  therefore,  not  a  vital 
part  of  education ;  since  "  education  is  not  preparation 
for  life,  it  is  life." 


CHAPTER  XII 

TESTING  RESULTS 

117.  Current  Forms  of  Test.  —  Testing  the  results  of 
a  teacher's  work  is  not  only  important,  but  it  is  also  a 
very  illuminating  thing  both  to  the  pupil  and  to  the 
teacher.  Tests  may  also  exert  a  powerful  influence  in 
determining  the  nature  of  the  instruction,  as  when  a 
class  has  to  be  prepared  to  take  an  examination  set  by 
authorities  outside  the  school,  and  hence  not  familiar 
with  local  conditions.  In  this  case,  the  teacher  is  very 
likely  to  study  the  syllabus  and  the  examination  papers 
of  the  past  years  and  to  cram  his  pupils  on  them.  In 
such  cases  the  test  evidently  does  far  more  harm  than 
good. 

The  questions  and  problems  at  the  end  of  each  chapter 
in  every  textbook  are  intended  to  serve  the  double  pur- 
pose of  giving  the  pupil  some  experience  in  applying  the 
information  acquired  from  that  chapter,  and  of  testing 
the  extent  and  the  definiteness  of  his  knowledge.  As 
has  been  stated,  most  teachers  are  continually  surprised 
at  the  difficulty  that  most  of  the  pupils  have  in  solving 
the  problems  and  in  answering  these  questions.  If  the 

270 


TESTING  RESULTS  271 

teacher  happens  to  give  a  new  type  of  problem,  one  not 
specifically  answered  in  the  book,  the  whole  class  will 
usually  be  floored  by  it.  They  "  have  not  had  that  kind 
before,"  and  cannot  find  the  formula  for  it. 

Ii  the  light  of  the  preceding  discussion,  the  reason  for 
this  is  not  hard  to  find.  Just  examine  the  questions  and 
problems  in  the  current  texts  and  examination  papers. 
This  is  the  sort  of  thing  you  find  in  plenty :  — 

The  volume  of  a  certain  mass  of  hydrogen  is  250  c.c. 
under  a  pressure  of  800  mm.  of  mercury.  What  is  its 
volume  under  standard  pressure,  760  mm.? 

A  weightless  rod  70  cm.  long  rests  on  a  fixed  point 
25  cm.  from  one  end.  To  this  end  a  weight  of  2  kgm.  is 
attached.  What  weight  must  be  hung  from  the  other 
end  so  that  the  rod  may  be  horizontal? 

If  a  body  moves  with  uniform  velocity  of  10  cm.  per 
second  for  20  seconds,  how  far  will  it  have  traveled  ? 

A  body  starting  from  rest  acquires  in  5  seconds,  with 
a  uniform  acceleration,  a  velocity  of  4900  cm.  per  second. 
WThat  is  its  average  velocity  ? 

A  force  of  5000  dynes  acts  for  10  seconds  upon  a  mass 
of  250  grams  which  is  free  to  move  and  starts  from  rest. 
What  momentum  is  imparted  to  the  body?  What  is 
its  acceleration?  How  far  will  it  move  in  10  seconds  ? 

The  weight  of  a  certain  mass  is  84  gm.  What  is  its 
weight  expressed  in  dynes  ? 


272  THE  TEACHING  OF  PHYSICS 

What  is  the  length  of  a  seconds  pendulum  whose  grav- 
ity acceleration  is  978  cm.  per  second  per  second? 

What  is  the  length  of  a  sound  wave  in  air  produced 
by  a  body  whose  frequency  is  384,  the  temperature  being 
20°  C.? 

A  brass  rod  is  50.8  cm.  long  at  20°  C.  and  59.886  cm.  long 
at  98  C.  Find  the  coefficient  of  linear  expansion  of  brass. 

What  is  the  specific  heat  of  a  substance  whose  tem- 
perature falls  60°  in  raising  the  temperature  of  the  same 
mass  of  water  12°  ? 

If  the  index  of  refraction  from  air  to  glass  is  1.5,  and 
light  is  incident  on  a  glass  plate  at  an  angle  of  45°,  what 
is  the  angle  of  refraction  ? 

How  many  joules  of  energy  does  a  kilowatt  hour 
represent? 

What  is  the  relative  resistance  of  90  cm.  of  platinum 
wire,  .4  mm.  in  diameter,  and  the  same  length  of  copper 
wire  .33  mm.  in  diameter,  the  specific  resistance  of  plati- 
num being  seven  times  that  of  copper? 

What  is  the  velocity  of  a  body  having  uniformly  ac- 
celerated motion  at  the  beginning  of  the  tth  second? 

Solve  both  equations  (2)  and  (3)  for  the  acceleration 
a  and  the  time  /. 

Using  the  formula  for  free  fall  and  that  for  work,  prove 
that  the  expression  of  kinetic  energy  should  contain 
velocity  squared. 


TESTING  RESULTS  273 

Two  forces  of  six  and  eight  dynes  respectively  act  at 
right  angles  to  each  other  on  a  mass  of  2  grams.  What 
is  the  resultant  force?  What  is  the  kinetic  energy  at 
the  end  of  3  seconds? 

118.  Questions  not  Significant.  —  This  collection  of 
problems  taken  from  "  standard  "  texts  and  college  en- 
trance examinations  might  be  extended  indefinitely.  It 
is  curious  that  authors  and  teachers  alike  seem  to  think 
that  pupils  want  to  know  the  answers  to  them.  As  a 
matter  of  fact,  the  pupils  are,  in  the  face  of  such  prob- 
lems, in  very  much  the  same  quandary  in  which  Mr. 
Dooley  found  himself  when  in  the  upper  berth  of  the 
sleeping  car.  After  pondering  on  "  how  a  man  could 
take  off  his  clothes  when  he  was  sitting  on  them,"  he 
asks :  "  and  what  should  I  do  with  them  when  I  got  them 
off?  "  Finding  no  satisfactory  answer  to  this  question, 
he  decided  "to  take  off  nothing  but  his  hat."  The 
pupils  would  surely  be  grateful  if  they  could  dispose  of 
the  question  of  what  to  do  with  the  answers  after  they 
got  them  in  so  summary  a  manner  as  this. 

It  is  clear  that  problems  of  the  sort  just  given  were 
made  up  to  be  problems  in  order  to  help  the  pupils  in 
becoming  familiar  with  the  facts  and  principles  of  ele- 
mentary physics.  They  correspond  to  no  reality,  and 
the  difficulties  involved  in  their  solution,  though  intro- 
duced to  give  discipline,  do  not  inspire  the  pupils  with 


274  THE  TEACHING  OF  PHYSICS 

an  eagerness  to  gird  themselves  up  to  overcome  them. 
They,  therefore,  give  little  transferable  training.  They 
are  not  very  likely  to  inspire  ideals  of  scientific  method  or 
respect  for  science.  Fortunately,  this  type  of  problem  is 
beginning  to  disappear  from  both  texts  and  examinations. 

119.  Vital  Problems  Needed.  —  The  questions  and 
problems  that  are  coming  in  to  give  the  pupils  practice 
in  thinking  and  real  discipline  in  overcoming  significant 
difficulties  are  of  the  following  kind:  — 

What  is  the  correct  position  in  dismounting  from  a 
moving  street  car?  Why? 

Why  does  an  automobile  tear  up  the  surface  of  the 
road  more  than  a  team  and  wagon  do? 

Why  do  you  stand  in  a  moving  car  with  your  feet  far 
apart? 

Why  are  there  doorknobs  on  doors? 

When  you  shovel  coal,  do  you  pull  up  on  the  shovel 
with  your  left  hand  as  hard  or  harder  than  you  push 
down  on  its  handle  with  your  right?  Why? 

When  you  sweep  a  rug  with  an  ordinary  broom,  does 
each  hand  do  half  the  work?  If  not,  show  which  hand 
does  the  more. 

How  much  work  do  you  do  when  you  go  up  a  flight  of 
stairs  10  feet  high? 

When  you  come  downstairs,  do  you  get  back  the  work 
done  in  going  up?  How? 


TESTING  RESULTS  275 

Why  does  lowering  the  handles  of  a  wheelbarrow  make 
it  easier  to  go  over  a  bump? 

Why  do  raindrops  make  inclined  streaks  on  the  win- 
dows of  a  railway  car  ?  In  which  direction  do  the  streaks 
slope  when  the  car  is  moving  east? 

If  you  weigh  125  pounds  and  can  just  float  with  your 
nose  out  in  fresh  water,  what  is  your  volume? 

Could  twenty-five  horses  make  an  automobile  go  as 
fast  as  a  twenty-five  horse-power  engine  can?  Why? 

What  makes  a  wood  fire  snap  and  crackle? 

Why  can  vegetables  be  cooked  more  efficiently  in  a 
fireless  cooker  than  on  a  red  hot  stove? 

What  prevents  a  pond  from  freezing  solid? 

Which  cools  faster,  a  cup  of  hot  tea  or  the  tea  that 
remains  in  the  teapot?  Why? 

What  is  the  dew  point  directly  under  the  lid  of  a  kettle 
of  boiling  water  ? 

Why  does  the  air  escaping  from  the  valve  of  a  bicycle 
tire  feel  cool? 

How  many  pounds  of  coal  does  your  furnace  burn 
daily?  How  many  B.  T.  U.  of  heat  are  liberated  in  the 
house  per  day?  How  many  foot  pounds  of  energy  does 
this  represent? 

Why  can  birds  perch  without  harm  on  electric  wires? 

Why  is  the  "  third  rail "  dangerous,  while  the  rails  of 
an  ordinary  trolley  track  are  not? 


276  THE  TEACHING  OF  PHYSICS 

Can  you  light  a  Christmas  tree  with  6-volt  lamps  if 
the  only  current  available  is  the  no- volt  city  current? 
How? 

Why  does  clapping  your  hands  make  a  noise  while 
waving  them  does  not  ? 

Why  should  colors  that  are  to  be  worn  in  artificial 
light  be  selected  in  the  same  kind  of  light? 

Does  placing  a  red  shade  over  an  alcohol  flame  colored 
with  salt  make  people  look  less  ghastly?  Why? 

What  makes  the  colors  in  a  soap  bubble  ? 

Why  has  no  one  ever  found  the  pot  of  gold  that  lies 
buried  at  the  end  of  the  rainbow  ? 

These  are  a  few  samples  of  the  many  questions  which 
have  some  chance  of  defining  significant  problems  for 
the  majority  of  the  pupils.  When  they  have  acquired 
some  skill  in  the  solution  of  such  problems,  it  may  be 
possible  to  make  more  abstract  problems  significant  to 
them.  Whenever  this  can  be  done,  it  is  well  to  do  it; 
but  it  is  practically  useless  to  begin  with  the  abstract 
problems  if  the  purpose  of  the  instruction  is  that  defined 
in  Chapter  IX. 

120.  Ordinary  Examinations  Inefficient.  —  Besides  the 
questions  and  problems  which  form  an  almost  daily  part 
of  the  course,  examinations  and  quizzes  given  by  the 
teacher  himself  may  be  made  of  great  importance  both 
for  the  pupils  and  for  the  teacher.  The  ordinary  form 


TESTING  RESULTS  277 

of  examination,  however,  in  which  the  pupils  try  to 
answer  questions  and  to  solve  problems  is  open  to  two 
serious  objections.  In  the  first  place,  it  tests  the  pupil 
in  too  many  ways  at  once.  His  answers  are  the  com- 
bined sum  of  the  activities  of  his  memories,  his  observa- 
tions, his  past  experiences,  his  present  condition,  and  so 
on.  In  the  second  place,  the  evaluation  of  the  pupil's 
paper  by  the  teacher  is  subject  to  a  large  error  due  to  the 
personal  equation.  The  grades  assigned  by  different 
teachers  to  the  same  papers  differ  widely.  Also  ability 
to  answer  examination  questions  is  no  sure  mark  of 
ability  to  think  scientifically. 

121.  More  Definite  Tests.  —  For  these  reasons  the 
teacher  who  wishes  to  test  his  own  work  in  order  to  dis- 
cover where  he  is  failing  and  where  succeeding  will  find 
the  ordinary  examination  a  rather  fickle  guide.  He 
needs  more  definite  and  more  quantitative  measures  of 
the  progress  of  the  pupils'  abilities,  and  this  measuring 
of  the  growth  of  human  abilities  is  at  best  still  an  uncer- 
tain and  precarious  task,  as  Thorndike  shows  in  his  Edu- 
cational Psychology.  But  notwithstanding  the  com- 
plexity of  the  problem,  considerable  progress  has  been 
made  toward  more  definite  methods  of  testing.  Among 
these,  Thorndike  suggests  the  following : 1  — 

1  Thorndike,  School  Science  and  Mathematics,  Vol.  XI,  p.  315,  April, 
1911. 


278  THE  TEACHING  OF  PHYSICS 

"  Knowledge  may,  however,  be  measured  more  conven- 
iently than  by  the  examination  of  notebooks,  essays,  or 
replies  to  questions  of  the  ordinary  sort.  These  have 
the  merit  of  adequacy  and  richness,  but  the  defects  of 
measuring  too  many  things  at  once  and  too  indefinitely. 
Greater  uniformity  in  the  use  of  the  test,  quickness  in 
scoring  it,  and  freedom  from  ambiguity  in  the  numerical 
value  assigned  can  be  secured  by  the  exercise  of  enough 
ingenuity.  I  will  mention  two  tests  as  samples  of  the 
many  that  are  possible.  The  first  is  an  adaptation  of  a 
test,  devised  by  Ebbinghaus  to  measure  mental  efficiency 
in  general,  in  filling  in  words  omitted  from  a  passage. 
From  even  the  hastily  devised  sample  presented  here  it 
will  be  seen  that  this  form  of  test  is  scored  with  reasonable 
ease.  The  speed  of  an  individual  in  selecting  words  to 
fill  the  gaps  and  the  appropriateness  of  his  selections 
together  measure  his  knowledge.  The  former  is  scored 
with  no  effort  at  all  and  the  latter  with  far  less  effort 
than  is  required  to  evaluate  answers  to  questions,  essays, 
or  experimental  work.  The  paragraphs  and  omissions 
therefrom  should  be  arranged  with  care  and  improved 
after  trial,  but  it  may  be  of  interest  to  some  of  you  to 
compare  the  ratings  obtained  in  six  or  eight  tests  of  five 
minutes  each  like  the  following:  — 

"  A  body  changing  its  position  in  space  moves  in  a  cer- 
tain..  ..at  a  certain..  ,  .A.  ..in  the 


TESTING  RESULTS  279 

called  acceleration.    To  change  either 

the or  the of  a  moving 

requires Suppose  a 

pound  of  lead  to  be  held  at  rest  500  feet  above  the  surface 
of  the  ocean  by  a  string  and  the  string  to  be  cut.    The 

body    will toward    the of    the 

beginning  to with  a 

of  just  barely  over 

and  reaching  at  the  end  of  one  second  a 

of feet  from  where  it  started.    In  one  sec- 
ond the will  have from 

to feet    per 

"  The  second  is  a  very  simple  development  of  so-called 
association  tests  which  I  have  used  with  good  success  in 
regular  examinations  in  psychology  for  a  number  of  years. 
It  needs  no  explanation  other  than  a  sample. 

"  Write  after  each  of  these  words  some  fact  which  it 
suggests  to  you :  — 

acceleration       gravity  current  lever 

density  expansion       elastic  inclined 

"  As  useful  means  of  measuring  the  interests  aroused  by 
the  study  of  science,  I  suggest  records  of  the  books  taken 
from  public  libraries,  of  the  periodicals  chosen  in  public 
reading-rooms,  of  the  collections  gathered  and  objects 
constructed  by  pupils,  and  a  modified  form  of  the  test 


280  THE  TEACHING  OF  PHYSICS 

just  described,  the  given  words  being  much  less  easily 
provocative  of  thoughts  about  facts  of  science,  and  being 
mixed,  if  necessary,  with  words  that  would  call  up  facts  of 
science  only  in  a  person  absorbed  by  scientific  interests. 
The  sample  I  give  is  left  without  such  padding  for  dis- 
guise. 

"  Write  after  each  of  these  words  some  fact  which  it 
suggests  to  you :  — 

work  time  wave  square 

positive  light  level  change 

water  rate  pull  book 

mass  study  transform  gas  . 

long  contract  heat  law 

"  This  latter  test  of  interest  should  be  varied,  using  pic- 
tures of,  say,  a  man  rolling  a  barrel  up  a  board  into  a 
wagon,  a  lightning  flash  in  the  sky,  an  ordinary  balance 
scale,  and  the  like,  with  a  similar  mixture  of '  innocent ' 
pictures.  Besides  words  and  pictures,  actual  or  described 
events  can  be  used.  If  such  association  tests  are  to  be 
used  to  measure  interest,  they  should  not  be  used  previ- 
ously in  the  form  calling  definitely  for  facts  about  science. 
These  tests  of  interests  may  be  used  to  measure  both 
special  interests  in  particular  sciences  and  general  inter- 
ests, as  in  fact  rather  than  fiction,  knowledge  rather  than 
opinion,  or  verification  rather  than  dispute. 


TESTING  RESULTS  281 

"  Of  other  means  of  measuring  the  general  changes 
wrought  by  the  study  of  science  I  will  mention  only  two.  y 
The  first  concerns  the  power  to  utilize  experience  well  in 
thought. 

"  What  is  needed  for  this  purpose  is  a  series  of  problems 
or  tasks,  relative  success  with  which  depends  as  much  as 
possible  upon  having  power  to  use  experience  and  as 
little  as  possible  upon  having  had  certain  particular  ex- 
periences. For  example,  relative  success  with  the  prob- 
lem, '  Which  is  heavier,  a  pint  of  cream  or  a  pint  of  milk  ?' 
is  determined  largely  by  ability  to  select  in  thought  the 
essential  fact  that  cream  rises  and  to  infer  its  obvious 
consequence.  The  data  themselves  are  possessed  ade- 
quately by  all,  or  nearly  all,  pupils  alike. 

"  To  get  such  problems  we  wrote  some  time  ago  to  one 
hundred  teachers  of  science,  half  in  universities  and 
colleges,  and  half  in  secondary  schools.  I  quote  some 
of  them :  — 

Raindrops  are  coming  straight  down.  Will  a  car 
standing  still  or  one  moving  rapidly  receive  in  one  minute 
the  greater  number  of  drops  on  its  roofs  and  sides  ? 

Is  air  drawn  up  a  hot  chimney  or  is  it  pushed  up  ? 

Since  it  is  possible  for  a  person  to  float  in  water  why  is 
it  possible  for  him  to  sink? 

A  cylinder  and  a  cone  equal  in  base  and  in  altitude  rest 
on  a  plane  surface.  Which  is  harder  to  tip  over? 


282  THE  TEACHING  OF  PHYSICS 

A  magnet  attracts  two  iron  nails.     If  the  magnet 
removed,  will  the  nails  attract  each  other? 

Is  it  harder  to  keep  your  hands  clean  in  the  winter  tha 
in  the  summer?  Why? 

How  many  surfaces,  corners,  and  edges  has  a  cube? 

Which  has  the  greater  surface,  a  cube  10  inches  o 
edge  or  a  sphere  10  inches  in  diameter  ? 

What  is  the  largest  mammal  in  the  world  ? 

Does  an  iron  ball  weigh  more  when  it  is  hot  than  whe 
it  is  cold  ? 

If  a  bottle  of  gas  which  is  lighter  than  air  be  place 
with  its  open  mouth  upward,  will  the  gas  escape  froi 
the  bottle  or  will  the  heavier  air  press  the  gas  back  int 
the  bottle? 

Is  an  incandescent  lamp  filament  on  fire? 
'»    Will  a  ship  that  will  just  barely  float  in  the  ocean  floa 
on  Lake  Erie  ? 

Will  a  pound  of  popcorn  gain  or  lose  weight  or  sta 
the  same  after  it  has  been  popped? 

"The  second  means  of  measuring  changes  in  genen 
power  to  think  is  an  adaptation  of  one  devised  by  Prc 
fessor  R.  S.  Woodworth,  in  which  the  pupil  picks  ou 
from  such  a  series  as  that  below  the  statements  that  ar 
logically  absurd,  not  possibly  true.  It  will  be  seen  tha 
statements  could  be  chosen  which  would  test  the  powe 
of  analysis  and  of  thinking  things  together  in  any  field  c 


TESTING  RESULTS  283 

science  from  the  most  specialized  to  the  most  universal. 
Following  is  an  example  of  this  form  of  test. 

Put  a  mark  in  the  margin  opposite  each  of  the  follow- 
ing sentences  which  is  absurd:  — 

Though  armed  only  with  his  little  dagger,  he  brought 
down  his  assailant  with  a  single  shot. 

Silently  the  assembly  listened  to  the  orator  addressing 
them. 

While  walking  backwards,  he  struck  his  forehead 
against  a  wall  and  was  knocked  insensible. 

I  saw  his  boat  cleaving  the  water  like  a  swan. 

Having  reached  the  goal,  I  looked  back  and  saw  my 
opponents  still  running  in  the  distance. 

Offended  by  his  obstinate  silence,  she  refused  to  listen 
to  him  further. 

The  one-armed  cripple  was  attacked  by  a  dog  which 
seized  his  wrist,  but  he  pushed  it  off  with  the  other  hand. 

With  his  sword  he  pierced  his  adversary,  who  fell  dead. 

While  threading  my  way  through  the  crowd,  I  came 
suddenly  upon  an  old  friend. 

The  storm  which  began  yesterday  morning  has  con- 
tinued without  intermission  for  three  days. 

The  dogs  pursued  the  stag  through  flower  gardens  in 
full  bloom. 

That  day  we  saw  several  icebergs  which  had  been 
entirely  melted  by  the  warmth  of  the  Gulf  Stream. 


284  THE  TEACHING  OF  PHYSICS 

While  sharpening  his  three-bladed  knife,  my  cousin 
cut  his  middle  finger. 

Our  horse  grew  so  tired  that  finally  we  were  compelled 
to  walk  up  all  the  hills. 

The  red-haired  girl  standing  in  the  corner  is  taller 
than  any  of  her  older  brothers. 

A  bricklayer  fell  from  a  new  building  quite  near  our 
house,  and  broke  both  his  legs. 

The  hands  of  the  clock  were  set  back,  so  that  the 
meeting  was  sure  to  close  before  sunset. 

Many  a  sailor  has  returned  from  a  long  voyage  to  find 
his  home  deserted  and  his  wife  a  widow. 

The  two  towns  were  separated  only  by  a  narrow  stream 
which  was  frozen  over  all  winter. 

"The  great  advantage  of  these  means  of  measuring 
intellectual  ability  lies  in  their  rapidity  and  ojectivity. 
If  well  devised,  only  two  answers  are  possible,  the  pupil 
is  measured  easily,  rapidly,  and  independently  of  sub- 
jective factors,  and  his  condition  is  defined  in  terms  of 
a  simple  numerical  value. 

"  There  is  no  time  for  me  to  discuss  methods  of  mak- 
ing, recording,  and  utilizing  these  or  the  hundreds  of 
other  equally  worthy  measurements  of  educational 
achievement,  that  is,  of  changes  produced  or  prevented  in 
human  nature.  Nor  is  this  a  proper  occasion  to  outline 
the  precautions  that  are  required  by  the  complexity  and 


TESTING  RESULTS  285 

variability  of  facts  of  intellect  and  character  and  the  ab- 
sence of  well-defined  scales  with  equal  units  and  known 
zero  points,  in  which  to  measure  facts  of  intellect  and 
character.  For  our  present  purpose  it  is  enough  to 
know  that,  in  spite  of  difficulties,  the  measurement 
can  be  made,  and  that  a  man  of  science  can,  if  he  will,  be 
as  scientific  in  thinking  about  human  beings  and  their 
control  by  education,  as  in  thinking  about  any  fact  of 
nature." 

Another  effective  form  of  test  consists  in  presenting 
to  the  pupils  a  simple  experiment,  and  asking  them  to 
write  brief  answers  to  the  questions :  I.  What  was  done  ? 
II.  What  happened?  III.  How  do  you  interpret  your 
observations  ?  The  teacher  makes  out  a  list  of  the  points 
that  are  important  to  observe  and  of  the  justifiable 
interpretations.  The  papers  are  graded  by  counting 
the  number  of  these  points  correctly  observed  and  in- 
ferred by  the  pupil.  For  example,  the  teacher's  state- 
ment of  a  perfect  paper  might  be :  — 

I.  An  empty  drinking  glass  was  inverted  and  pushed 
down  into  a  large  beaker  half  full  of  water. 

II.  The  level  of  the  water  was  lowered  inside   the 
drinking  glass  and  raised  outside  of  it. 

The  level  inside  was  slightly  above  the  rim  of  the 
drinking  glass. 

III.  Air  is  a  substance  that  occupies  space. 


286  THE  TEACHING  OF  PHYSICS 

The  pressure  on  the  air  inside  the  glass  was  increased 
by  an  amount  measured  by  the  difference  in  level  be- 
tween the  water  surface  inside  and  that  outside. 

The  air  was  compressed  by  this  increase  of  pressure. 

If  a  series  of  fifteen  tests  of  this  sort  were  given  through- 
out the  year,  a  teacher  could  get  a  fairly  definite  measure 
of  the  progress  of  each  pupil  in  powers  of  observation, 
analysis,  and  inference.  The  value  of  such  a  series  would 
be  vastly  increased  if  a  group  of  fifteen  or  twenty  teachers 
would  cooperate  in  planning  the  series,  in  deciding 
which  are  the  essential  points  of  each  test,  and  in  grading 
the  papers.  If  the  superintendents  of  schools  in  large 
cities  would  encourage  the  physics  teachers  under  their 
care  to  organize  and  carry  out  such  a  series  of  tests  each 
year,  the  results  would  be  of  vastly  greater  educational 
value  than  those  now  obtained  by  supervision  and  the 
ordinary  form  of  written  examination. 

122.  Tests  Help  the  Teacher.  —  The  results  of  this 
kind  of  tests  are  also  illuminating  to  the  teacher.  We 
all  assume  that  pupils  see  in  our  experiments  the  points 
we  intend  to  illustrate.  This  is  by  no  means  the  case. 
These  tests  give  us  a  very  direct  means  of  finding  out  what 
pupils  do  observe  and  how  they  do  reason;  and  it  is 
this  information  that  is  most  needed  at  present  to  enable 
us  to  organize  courses  adapted  to  the  abilities  of  the 
pupils.  Our  chief  efforts  in  the  past  have  been  directed 


TESTING  RESULTS  287 

to  devising  ways  and  means  of  making  children  swallow 
a  logically  determined  body  of  knowledge  called  the  facts 
and  principles  of  elementary  physics.  Our  present  prob- 
lem is,  (i)  to  find  out  how  the  pupils  actually  do  observe 
and  think,  and  (2)  to  discover  by  experiment  how  the 
material  of  physics  may  be  used  most  effectively  to 
develop  ideals  of  scientific  method  while  acquiring  a 
mastery  of  the  most  useful  physical  principles. 

123.  Summary.  —  The  conclusions  to  which  the  dis- 
cussion of  the  preceding  pages  point  may  be  stated  as 
follows :  i.  The  "  faculty  psychology  "  with  its  doctrine 
of  formal  discipline  has  been  shown  to  be  inadequate 
because  of  its  neglect  of  the  emotional  factors  of  conduct. 
2.  Educational  theory  has  progressed  to  the  point  where 
it  is  able  to  offer  a  fairly  definite  set  of  working  hypothe- 
ses for  democratic  education.  3.  The  time  has  therefore 
come  to  test  these  working  hypotheses  by  careful  ex- 
perimentation in  classes  under  normal  school  conditions. 
4.  Such  experimentation  requires  the  cooperation  of 
groups  of  teachers,  and  a  more  definite  testing  of  results 
than  is  possible  by  the  ordinary  form  of  written  examina- 
tion. 5.  This  much-needed  experimentation  should 
be  directed  to  solving  two  problems,  namely,  what 
material  from  physics  is  most  effective  for  purposes  of 
general  education,  and  what  is  the  most  effective  way  of 
presenting  and  using  that  material  ? 


288  THE  TEACHING  OF  THYSICS 

124.  More  Efficient  Teaching  Demands  Educational 
Experiments.  —  The  supremacy  of  the  classics  and 
mathematics  in  the  school  world  is  due  in  large  measure 
to  the  long  process  of  refinement  to  which  the  methods 
of  teaching  them  was  subjected  during  the  centuries 
in  which  they  formed  the  mainstay  of  aristocratic 
schooling.  These  methods  were  perfected  by  a  lengthy 
process  of  trial  and  error,  and  are  fairly  well  adapted  to 
the  homogeneous  class  of  professional  men  for  whom 
they  were  devised  and  to  whose  professional  interests 
they  are  closely  related. 

Correspondingly  efficient  methods  of  teaching  the 
subjects  that  have  recently  been  added  to  the  curriculum, 
in  response  to  the  demands  of  democratic  education,  have 
not  yet  been  devised.  The  students  of  to-day  are  no 
longer  parts  of  a  relatively  homogeneous  class,  but  make 
up  an  extremely  heterogeneous  mass  with  widely  diver- 
sified interests,  motives,  and  needs.  Their  demands  are 
insistent  and  pressing,  so  there  is  not  time  to  develop 
the  methods  of  teaching  the  newer  subjects,  of  which 
physics  is  one,  by  the  long  process  of  trial  and  error 
used  in  the  case  of  the  classics. 

The  remarkable  progress  made  by  the  science  of 
physics  in  the  last  twenty-five  years  is  due  in  large 
measure  to  the  ever  increasing  amount  of  laboratory 
work  that  has  been  done.  In  like  manner,  we  may  look 


TESTING  RESULTS  289 

for  an  accelerated  progress  in  methods  of  teaching 
physics  as  soon  as  physics  teachers  begin  a  laboratory 
study  of  their  methods  of  teaching.  As  in  physics, 
so  in  education,  the  first  essential  for  efficient  laboratory 
work  is  a  system  of  suitable  units  and  methods  of  meas- 
urement. Such  a  system  cannot  be  established  without 
a  vast  amount  of  labor  and  a  generous  cooperation  among 
those  who  are  working  for  its  establishment.  If  this 
book  shall  be  the  means  of  arousing  some  physics  teachers 
to  the  nature  and  the  immediacy  of  the  problem  before 
us,  and  of  stirring  them  to  devote  some  attention  to  the 
laboratory  study  of  this  problem,  its  purpose  will  be 
fully  accomplished. 


BIBLIOGRAPHY 

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DYSART,  P.  M.    A  Most  Effective  Method  of  Discouraging  Good 

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ELIOT,  C.  W.    Laboratory  Teaching.    School  Science  and  Mathe- 
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HALL,  EDWIN  H.  Modern  Trend  of  Physics  Teaching.  Edu- 
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JAMESON,  J.  M.  More  Interesting  and  Practical  Mechanics  for  the 
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MAGIE,  W.  F.  The  Primary  Concepts  of  Physics.  Science, 
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295 


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INDEX 


Abstract,  the,  87,  137,  168,  254,  263. 
Acceleration,  34,  36,  151,  157,  160,  207. 
Action,   principle  of  least,    159,   224; 

and  reaction,  156,  224. 
Adams,  G.  B.,  105. 
Administration,  of  schools,  202. 
d'Alembert,  principle,  159. 
Applications,  place  of,  141,   I99>   267. 
Approximation,  144,  232. 
Arabians,  118. 
Archimedes,  118,  133,  153- 
Aristotle,  25,  96,  100,   112,  118,  120, 

131,  135,  147,  171- 
Arnott,  N.,  38. 
Association  of  ideas,  140,  214;   tests, 

280. 

B 

Bacon,  Roger,  25,  120. 

Bagley,   W.   C.,    189,    199- 

Bergson,  Henri,  100. 

Bouasse,  H.,  25,  122. 

Brewster,  David,  28,  31. 

British  Association  for  the  Advance- 
ment of  Science,  abuses  of  syllabi, 
70. 

Brown,  E.  E.,  i,  6,  29,  31. 

Bureau  of  Education,  United  States, 
Bulletins  on  Physics  Teaching,  41 
sq. 

C 

Carlyle,  Thos.,  114. 

Carnegie  Foundation,  203. 

Carnot,  Sadi,  164,  223. 

Causal  Principle,  153,  209. 

Central  Forces,  doctrine  of,  157,  219, 

222. 
Chamberlain,  H.  S.,  n,  135- 


Chicago  University,  new  Entrance 
Requirements  at,  23. 

Church  of  Rome,  107. 

Clarke,  F.W.,  41- 

Classics,  method  of  the,  172,  288. 

Coleman,  S.  E.,  248. 

College  Entrance  Examination  Board, 
Syllabus  of  the,  66,  71. 

College  Entrance  Requirements,  sub- 
jects suited  for,  12;  Committee  on, 
14  sq.,  60;  new,  at  Harvard  and 
Chicago,  23;  Physics  in,  30,  45; 
idea  of,  174;  uses  of,  262. 

Commerce,  development  of,   104. 

Committee  of  Ten,  9  sq. ;  on  College 
Entrance  Requirements,  14  sq.,  41 ; 
Conference  of  Physics  of,  59;  For- 
mal Discipline  in,  14,  170,  175. 

Comstock,  J.  L.,  32. 

Concrete,  the,  87,  137,  168,  177.  253, 
263. 

Conservation  of  Energy,  53,  86,  164, 
210,  223,  237,  266. 

Crusades,  108,  no. 

Culture,  174,  193. 


Definitions,  current  forms  of,   76  sq.t 

94;   justification   of,    225   sq. 
Descartes,  158. 
Descriptive  List,  Harvard,  54  sq.t  247, 

251- 
Dewey,  John,  74,  116,  133,  136,  137, 

141,   173,   187,   192,   195,   201,   211, 

253,  263,  267. 
Discipline,    Plato    on    mental,     100; 

Formal,  doctrine  of,  170,  179,    184, 

196,  268,  287;  in  Physics,  176,  213; 

transfer  of,  179,  190;   Specific,  184, 


301 


302 


INDEX 


213;     Motivation  and,    194,    200, 

215. 

Draper,  J.  W.,  39- 
Duhem,  P.,  25,  221. 


Efficiency,  definition  of,  230;  ther- 
mal, 234;  mental,  tests  for,  278. 

Electricity,  treatment  of,  237,  243, 
258. 

Elements,  identical,  185,  196,  207,  214. 

Elimination,  of  Students  from  High 
Schools,  21. 

Emotions,  place  of,  171,  183,  191,  198, 
268,  286;  in  ideals,  100,  199,  250. 

Energetics,  167. 

Energy,  Conservation  of,  53,  164,  210; 
in  commerce,  166,  210;  in  the  course, 
186,  198,  210,  219;  principle  of,  220, 
223,  226,  237,  266;  definition  of, 
235- 

English,  discipline  in,  173. 

Examinations,  by  external  body,  202, 
262,  270;  uses  and  abuses  of,  70, 
204,  277. 

Experimentation  in  education,  205, 
286  sq. 

F 

Faculty,  psychology,  171,  179,  287. 

Falling  Bodies,  Laws  of,  36;  Aristotle 
on,  101;  Galileo  on,  101,  150;  New- 
ton on,  156. 

Feeling,  place  of,  171,  183,  191;  of 
wonder,  192,  198,  212,  214. 

Ferguson,  Jas.,  28,  31. 

Force,  Newton  on,  157,  160,  219; 
measurements  of,  162,  225;  defini- 
tion of,  229. 

Foreign  Languages,  work  in,  172,  194. 

Formal  Discipline,  doctrine  of,  14, 
170,  179,  190,  196,  255;  in  Physics, 
176,  212. 

Forms,  mathematical,  in  Physics,  25, 
34,  38,  177,  209. 

Forrest,  J.  D.,  106. 

Franklin,  Benj.,  2,  29. 

Franklin,  W.  S.,  75. 

Fundamental  principles,  222. 


Galileo,  26,  101,  120,  131,  150  sq., 
224,  232. 

Generalized  bodies,  88,  94. 

Geometry,  truth  of,  145,  219;  disci- 
pline of,  1 80. 

Germanic,  industry,  u,  116  149; 
and  science,  113,  144,  209. 

Germans,  scientific  method  of,  113, 
147. 

Greeks,  scientific  method  of  the,  97, 
112,  220;  philosophy  of,  102,  116, 
125,  147;  doctrine  of  Formal  Dis- 
cipline, 170,  183. 

Guttenberg,  120. 

H 

Habit,  distinguished  from  ideal,   189. 

Hall,  E.  H.,  and  Bergen,  Textbook, 
56,  62,  248. 

Harvard,  New  Entrance  Requirements 
at,  23 ;  Descriptive  List,  54  sq.,  65, 
247. 

Heat,  measurement  of,  165;  treat- 
ment of,  1 86,  233  sq.,  laboratory 
problems  in,  257. 

Heck,  W.  H.,  171,  204. 

Helmholtz,  H.  von,  103,  165. 

Henderson,  C.  H.,  194. 

High  Schools,  purpose  of,  2 ;  early,  3 ; 
growth  of,  5 ;  statistics  of  small,  19 ; 
elimination  from,  21;  Natural  Phi- 
losophy in,  27  sq. 

Huyghens,  Chr.,  158,  224. 


Ideals  of  Method,  189,  199,  212,  214, 

239,  250,  262,  274. 
Identical  elements,  theory  of,  185,  196, 

207,  214. 
Individual  differences,  neglect  of,  181, 

204,  265. 

Inductive  Teaching  of  Physics,  46. 
Industrial    Education,    Massachusetts 

Commission   on,    22;    and   science, 

200,  212. 
Industry,    importance     of,     104    sq. ; 

method  of,  108,  212 ;  Germanic,  in, 


INDEX 


3°3 


116,   123,  209;  scientific,  tax,  200; 
energy  in,  166,  187. 

Intuition,  place  of,  133   sq.,  154,  168, 
209,  216,  227,  238,  268. 


Jones,  Wm.  C.,  14. 
Joule,  J.  P.,  164,  235. 


Kelvin,  164,  221. 


Laboratory  work,  42,  49,  74,  92,  205, 
218,  232,  246  sq.,  269,  288;  man- 
uals, 92,  248,  252 ;  suitable  problems 
for,  256. 

Lagrange,  159,  161. 

Languages,  work  in  foreign,  172,  194. 

Lavosier,  224. 

Laws,  of  Falling  Bodies,  34,  36 ;  New- 
ton's, of  Motion,  53,  156,  160,  162; 
precede  experiment,  83;  truth  of 
physical,  144. 

Lincoln,  A.,  177. 

Logic,  place  of,  133  sq.,  161,  167,  171, 
199,  209,  213,  216,  227,  238,  266,  268. 

M 

Mach,  E.,  152. 

Machines,  efficiency  of,  231. 

Mass,  157,  161 ;  conservation  of,  224. 

Massachusetts  Commission  on  In- 
dustrial and  Technical  Education, 
22. 

Mathematics,  in  Physics,  25,  34,  38, 
175,  209;  discipline  of,  180,  184, 
288;  definitions  of,  227. 

Mayer,  J.  R.,  164,  223. 

Mechanism,  uses  of,  220  sq.;  of  light, 
243- 

Memory,  discipline  of  the,  172,  179. 

Mental  Discipline,  Plato  on,  100;  of 
science,  126,  175,  215;  doctrine 
of,  170,  179,  190,  196,  255;  Motiva- 
tion and,  194,  215. 


Method,  ideals  of,  189,  199,  212,  214, 

239,  250,  262,  274. 
Monroe,  P.,  171. 
Moore,  A.  W.,  98. 
Motives,    in   defining   problems,    132, 

183;    and  discipline,  194,  215,  262. 

N 

National  Education  Association, 
Committee  of  Ten,  9,  59;  Commit- 
tee on  College  Entrance  Require- 
ments, 14,  60;  Committee  on  Ar- 
ticulation of  Schools  and  Colleges, 
24. 

National  Physics  Course,  the,  60,  64. 

Natural  philosophy,  28  sq. 

Newcomen,  234. 

New  Movement  among  Physics 
Teachers,  64. 

Newton,  Laws  of  Motion,  53,  156,  167, 
207,  216,  223;  Principia,  82,  158, 
159,  163,  177;  universal  gravitation, 
132;  work  of,  155  sq.,  182;  on 
force,  157,  1 60,  219;  central  forces, 
157,  219. 

New  York,  State  Syllabus,  65. 

North  Central  Association  of  Colleges 
and  Secondary  Schools,  Physics 
Syllabus  of  the,  67,  72,  206. 


Optics, 
266 


treatment  of,   239 
P 


258, 


Parker,  R.  G.,  32. 

Perpetual  Motion,  154,  158  sq.,  166, 

x68. 

Philosophy,  Natural,  28  sq. 
Physicist,   preparation  for  the  career 

of  a,  211,  239. 
Plato,  96  sq.,  147. 
Platonic  Thought,  100,  104,  115,  133, 

136,   144,   149,   171,   186,   196,   209, 

220,  237,  268. 
Poincare,  H.,  27,  134,  I45>  219,   222, 

225,  226,  244,  253. 
Problems,  abstract,  88,  271 ;    suitable, 

for  tests,  274,  276;  how  defined,  131, 


3°4 


INDEX 


140,  143,  229,  255;  of  nature,  183; 
in  education,  207,  scientific  method 
of  solving,  212;  suitable  for  labora- 
tory, 256  sq. 

Projectiles,  Galileo  on,  155. 

Psychological  order,  267. 

Psychology,  faculty,  171,  287;  and 
Formal  Discipline,  178. 

Ptolemy,  119. 

Q 

Quackenbos,  33,  43. 


Relatedness  of  phenomena,  154,  158, 
166,  168,  209,  216,  225,  237. 

Remsen,  I.  M.,  73. 

Renaissance,  117. 

Romans,  and  scientific  method,  104; 
formal  discipline  among,  170. 

Rumford,  163. 

S 

Scientific  method,  of  Greeks,  97,  112; 
of  Germans,  113  sq.,  144;  of  indus- 
try, 122,  210;  of  Physics,  125,  133, 
142,  210;  definitions  of  the,  127  sq. ; 
identical  elements  in,  186;  ideals 
of,  189,  199,  212,  239,  262;  in  edu- 
cation, 205. 

Scientific  training,  126,  212,  216. 

Simplicity  of  course,  218,  244. 

Shakespeare,  173. 

Snell,  W.,  120. 

Steam  engine,  163,  234. 

Steele's  Fourteen  Weeks,  42. 

Stevin,  224. 

Subject  matter,  identical  elements  in, 
1 86,  196,  214. 

Syllabus,  The  First,  51;  Harvard 
Descriptive  List,  54  sq.;  of  Com- 
mittee of  Ten,  60 ;  of  Committee  on 
College  Entrance  Requirements,  62  ; 
New  York  State,  65;  College  En- 
trance Examination  Board,  66; 
North  Central,  67,  72,  206;  uses  of, 
69,  204,  216,  262. 


Ten,  Committee  of,  9  sq.;   conference 

of  Physics  of,  59. 
Tests,  270  sq. ;   Ebbinghaus,  278. 
Textbooks,   73  sq.,   208,   273. 
Theories,  general,  89,  94,  242. 
Thorndike,  E.  L.,  178,  181,  204,  277. 
Thought,  Platonic,  100,  104,  115,  133, 

136,   144,   149,   171,   186,   196,  209, 

220,  237,  268. 

Training,  scientific,  126,  212. 
Transferable  training,    126,   212,    216. 
Transfer,  of    training,   179,   184,    196, 

212,  239,  250,  274;    of  ideals,  190, 

214. 
Truth,  of  physical  laws,  144,  209;    of 

geometry,  145. 


U 

U.  S.  Bureau  of  Education,  Bulletins 
on  Physics  Teaching,  41  sq. 

Units,  for  College  Entrance,  n,  18, 
202,  208;  constant  ratios  among, 
for  work,  heat,  electricity,  165,  219, 
236;  for  measuring  human  achieve- 
ment, 285,  289. 

Unity,  of  course,  218,  220,  244. 

University,  research  in  the,  8;  Phys- 
ics in  the,  25,  170. 


Velocities,  virtual,  159. 


W 

Watt,  Jas.,  163,  234. 

Wead,  C.  K.,  41. 

Wonder,  mother  of  science,  116,  123, 
136,  209;  feeling  of,  192,  198,  212. 

Woodhull,  John  F.,  29,  31,  39. 

Woodworth,  R.  S.,  tests,  282. 

Work,  principle,  158,  159,  232;  posi- 
tion of,  168;  definition  of,  228. 


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